𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, February 18, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Sat 19 Feb 02:41:17 GMT 2022 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2022/02/18/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmT1WmWT8oyJF7h6FDnkDWXE6tEV7sUdo6MyboEn1kLiFx Qmd7o1W8PgtXmeAFmAGFoVreMpLA1AVtvVjUMvVr7zc1YQ Qma88nEdV64rLJsqR8uVd62B8zwrDvuX6Etg42wsovLPUQ QmWMn5rx4mwf86jmAsH6KUasKtr2WVybRVa9b2sJECtwpz QmS1wrYoYvTPNPTvZYppVeYPXTR8rHjtMkwCEYGCEaEWUU QmTLUpA1Pbmatf5PSQgBbMk1Hj8eJFQAcNy7ahAe769Anx QmbQWJTJVwCBMn6Bc7J9W2fhZtZYwQh4SrKoy4dF1Rj3Pm QmZ3Z9HPLFuFUYdDqN8YY1cZW5M8k9MCEyfwYQiJSBdgg9 Qme1XwuhK1F1t6m8AJGPXQ8U9wCeB9UCDmmkPBEmWLharx QmQdk83ourWknf8WYXr4Z6LnuaLWYmqhpidR9Crga89wZn Qmae8sev1AAiuQdXEbMcdP8Nmxxz3DL81fAkGoiVLghjbB QmYBkNNgDtvjiZGy3f7RwY487FEsQEUQkXJN3yYkKnMGUa QmdmWehA6h2EsxLvmLQHxv9wFn9VZJZHVbgXQXVigmyUCo QmbqzbFLBLnEsD6wqjgRecqxx1eMiGqj8KkJ8LBeVS7kMR QmRogUf31QThSc3fc9qKNWAZGJTDSwdv1pupuEmsuUuu26 QmZRqBo3ysfz1YXExEqVuEuy5xb4ME8cK3jBDpd8wGSwwX QmT6UzkVGBqiGJqW9tNXHnJ2F7GjgkFTQ1tvxxFeYF4VH3 QmfSu9XMsGzj9YkPDP79UmwB6R9G9p3HQjsSCvUovR8y4o QmeC7QgpY53w9VR36JGVyYSzhMZkHLkGiYWgd57Dskr9pH QmZHDDpdkiKdpvVjLb94b8X2LhPVMcNQweiDqukj1DyKVT QmPgCJca3XFthf3S9xSXFzx2JdpEDjUZ3HPfAnGbLWi5kr ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ António Campinos Wants to Undo His Father’s Legacy for Several More Years, Spreading Corruption Across Europe and the World | Techrights ⦿ BREAKING NEWS/EXCLUSIVE: António Campinos Confirms That He is Seeking Reappointment | Techrights ⦿ FFII: In PL Holdings, European Court of Justice Confirms EU Law Cannot be Outsourced to International Courts Like Unified Patent Court (UPC) | Techrights ⦿ List of Currently Active Gemini Capsules on the Internet | Techrights ⦿ IRC Proceedings: Thursday, February 17, 2022 | Techrights ⦿ Linux Foundation Board in 2022: 86% Corporate and 81% Proprietary Software Companies | Techrights ⦿ Rest Assured the Linux Foundation Does Not Really Speak for Linux (Not Anymore) | Techrights ⦿ LXer Not Reachable Since February 16th (Updated) | Techrights ⦿ [Meme] Megaphone of António Campinos | Techrights ⦿ [Meme] A ’Social Democracy’ Where Every Vote is for Sale | Techrights ⦿ When AMD Sends You a Crate of CPUs Worth (Market Value of) Roughly $500,000 | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/02/18/antonio-campinos-corruption/#comments http://techrights.org/2022/02/18/antonio-campinos-reappointment/#comments http://techrights.org/2022/02/18/ffii-on-pl-holdings-upc/#comments http://techrights.org/2022/02/18/gemini-capsules-on-the-internet/#comments http://techrights.org/2022/02/18/irc-log-170222/#comments http://techrights.org/2022/02/18/linux-foundation-board-2022/#comments http://techrights.org/2022/02/18/linux-hostile-foundation/#comments http://techrights.org/2022/02/18/lxer-not-reachable/#comments http://techrights.org/2022/02/18/megaphone-for-campinos/#comments http://techrights.org/2022/02/18/meme-a-social-democracy-where-every-vote-is-for-sale/#comments http://techrights.org/2022/02/18/phoronix86-amd/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/02/18/easy-3-4-1-soon/#comments http://techrights.org/2022/02/18/rednotebook-2-23/#comments ䷩ 𝚕𝚒𝚗𝚎 78 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/antonio-campinos-corruption/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/antonio-campinos-corruption/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ António_Campinos_Wants_to_Undo_His_Father’s_Legacy_for_Several_More_Years, Spreading_Corruption_Across_Europe_and_the_World⠀✐ Posted in Europe, Patents at 3:10 pm by Dr. Roy Schestowitz Video_download_link | md5sum ffb2a8b0327f8592a584f33af5a5edc5 EPO Covering Up After 13 Years Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/epo-mafia-buying-time.webm Summary: The so-called ‘Mafia’ at the EPO (the staff of the EPO calls it “the Mafia”) doesn’t want to let go; perhaps in an act of cover-up — basically ensuring nobody outside the Mafia gets access to checks and balances — there’s already an approach for the Government of Portugal to cement a second term for the controversial Frenchman (whose father had come from Portugal and stayed in France to dodge political persecution) THE low blow to Alison Brimelow [1, 2] is the succession by the same sort of Mafia she had warned about and had personally suffered from (she later stepped down, almost understandably, leaving the EPO without leadership for quite some time). “The future of Europe is at stake because EPO corruption is like a cancer that spreads far beyond the Office and has already infested the Commission.”That Benoît_Battistelli ruined the EPO for 8 years is bad enough; what if António Campinos is allowed to do the same? We might soon be in an agonising scenario where in a period of 25 years more_than_85%_of_the_time_the_EPO's_President_was in_effect_French. Is this “diversity”? But it’s not even about nationality but about a cabal conspiring to break the law for personal gain, mostly for the benefit of litigation (at the expense of science, which Team UPC doesn’t exercise; it’s all about lawsuits or doing to the courts what they did to the EPO, i.e. to examination guidelines — nowadays rendered a production line or rubber-stampers, beholden to coup plotters instead of the EPC). This coming weekend we plan to say a lot more about patents. The_state_of_news about_patents_is_beyond_a_farce. The very same firms that hijacked — albeit by proxy — the EPO (they also want to do the same to courts) have taken over more than 90% of what one finds in the so-called ‘media’. This leads to a state of “alternative realities”, imposed by an echo chamber wherein litigation lobbyists preach to their choir, mentally masturbating to the tune of intentional lies (such as UPC being beneficial to SMEs). The future of Europe is at stake because EPO corruption is like a cancer that spreads far beyond the Office and has_already_infested_the_Commission. █ ䷩ 𝚕𝚒𝚗𝚎 147 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/antonio-campinos-reappointment/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/antonio-campinos-reappointment/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ BREAKING_NEWS/EXCLUSIVE:_António_Campinos_Confirms_That_He_is_Seeking Reappointment⠀✐ Posted in Europe, Patents at 12:45 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇A hardcore António Campinos⦈ Summary: António_Campinos confirms that he is seeking a renewal of his mandate and emphasises that he is seeking the endorsement of the Portuguese and not the French government Today it was unofficially revealed that EPO President António Campinos is seeking reappointment as EPO President for a second term. EPO insiders report that during an in-house video-conference Campinos responded to questions from staff by confirming that he is actively seeking reappointment. However, his attempt to secure a second mandate is subject to him obtaining the endorsement of “his” government. He was at pains to emphasise that this referred to the Portuguese and not the French government! 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Battistelli and Kongstad⦈ The inauguration of the new Portuguese government has been delayed_until_mid-March due to the need for a partial rerun of voting after a court decision which declared that more than 157,000 expatriate votes from 139 voting stations across Europe were invalid. So it could take some time before Campinos finally gets the green light from “his” government to pursue his plans for an extension of his EPO appointment. Campinos took over at the helm of the EPO in July 2018 after having been appointed for a five-year term. Thus, his current term is due to expire next year on 30 June 2023. It is expected that the EPO’s Administrative Council will discuss the renewal of his mandate at its 170th meeting scheduled to be held on 22_March_2022. (warning: epo.org link) If Campinos were to fail to secure the approval of the Portuguese government together with the backing of three-quarters of the delegations on the Council, then this would require the opening of a selection procedure to choose a successor. In the event of such a situation materialising, the Council could be expected to open the selection procedure at its June 2022 meeting. “The reason for this is that back in 2009/2010, the Council encountered great difficulties in arriving at a consensus and the election process was widely criticised for its lack of transparency.”However, the history of the EPO over the last decade or so has made the Council cautious about conducting such a procedure and it does its best to avoid it whenever it can. The reason for this is that back in 2009/2010 [PDF], the Council encountered great difficulties in arriving at a consensus and the election process was widely criticised for its lack of transparency. Leading the chorus of criticism about the lack of transparency was the outgoing President herself, Alison Brimelow who began her rebuke to the Council with the following words: “As President and the guardian of the EPC, I have to bring a problem to your attention.” Brimelow deplored the fact that those outside the closed circle of delegates participating in the confidential “C-point” discussions on the election of a new President had no clear idea of what had been decided and that these decisions were not made available to the wider public. Even IAM which normally restricts its coverage of EPO affairs to churning out uncritical puff-pieces had the following to say [PDF] after Benoît_Battistelli had finally managed to secure election in March 2010: “One of the striking aspects of the election process was its complete lack of transparency. Although all four candidates did go on the record about why they were standing and what their priorities would be as EPO president, at no stage was there any news about which countries were voting for which person and why. Even when Battistelli was elected there was no statement from the Administrative Council that explained the reasons for giving him the job.” In June_2014 (local_copy [PDF]), a year before Battistelli’s term of office was due to expire, the Council – led by Battistelli’s “protector” the notoriously corrupt Jesper_Kongstad – decided to extend the Corsican despot’s mandate by another three years in order to save themselves the bother of having to conduct a selection procedure to find a successor. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Cuno Tarfusser⦈ When the time finally came to elect a successor to Battistelli in_2017, the Council adopted a much more cautious approach than it had done in 2009. This time there was, for all intents and purposes, only one candidate, António Campinos. The disgruntled_Italian_delegation which felt that it had been cheated of a Vice-President position in 2012 due Battistelli’s sponsorship of Željko Topić tried to field an opposing candidate in the person of Cuno_Tarfusser. But Tarfusser’s “lack of an IP background” – compared to the self-styled “trademark expert” Campinos – was used to undermine his candidacy and ensure that Battistelli’s designated successor got the job. 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇IAM_propaganda⦈_ EPO propaganda organ IAM joined in efforts to discredit Tarfusser by pointing to his lack of an “IP background”. Now that Campinos is gradually approaching the end of his first term of office, the Council is probably keen to reappoint him in order to avoid the “disruption” of having to organise a new selection procedure. “Now that Campinos is gradually approaching the end of his first term of office, the Council is probably keen to reappoint him in order to avoid the “disruption” of having to organise a new selection procedure.”However, it remains to be seen whether the growing unrest among EPO staff and the impending threat of industrial_action by the staff union SUEPO will derail the Portuguese Pretender's plans to secure a second term of office. Watch this space… █ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆⣿⣀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡄⠀⣤⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠅⠋⠋⠁⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣿⣿⣿⡟⢃⠀⠀⣠⡀⠀⠀⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡁⠀⠀⠹⠇⠀⢠⣿⢟⡋⠁⠀⠀⢸⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢸⣿⠸⠁⠀⠒⠀⢘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⠿⠿⠿⣿⡿⠶⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⡿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣖⣴⣤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣆⣤⣄⣤⣴⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠰⠆⠀⠀⠀⡠⢠⣿⠉⠨⠟⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠛⠁⠀⠉⠀⣠⣶⡄⠀⠀⡈⣂⣀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢠⣿⠾⣷⠶⠆⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣤⣄⣀⠄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣴⡿⢁⣀⢶⣾⣿⣿⣿⣿⣧⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⡶⢶⡶⠶⠖⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠿⣛⠿⣿⣯⣍⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣤⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠭⠂⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠋⠃⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⣩⣻⣴⡶⢟⣂⣈⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⡏⠄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣻⣟⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣣⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⢾⣿⠿⣿⣛⣛⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠭⢛⡟⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣟⠓⢾⡙⠃⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣸⣿⣿⣿⠟⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠿⣿⢿⣿⣿⡿⠿⠯ ⠀⠀⢠⡄⡀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠆⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠿⠶⢙⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣳⡚⡷⢶⠚⢛⣺ ⠀⢀⣼⣧⡧⡧⣧⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢛⡠⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢨⡟⠡⠫⠷⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⠏⠈⠭⠝⡀⠈⠉ ⠀⠀⢨⣤⠇⠴⢦⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣡⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⡀⠀⠈⢵⡀⠶⠟⢀⣼⣿⢻⣿⣿⣿⣿⣿⣿⡧⠻⠿⠟⣉⣃⣉⡁⠁⠀ ⠀⠀⢸⡀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣛⣛⠛⠛⠛⠿⠟⠛⢻⣿⣿⠿⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⡠⠊⠀⠀⠀⠸⣿⣶⠔⣸⠟⠋⣼⣿⣿⣿⣿⣿⣿⡃⣤⣶⠾⠻⠟⠋⠁⠀⠈ ⠀⠀⢸⡛⡂⢻⣿⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣿⣿⣿⣿⣷⣶⣶⣦⣄⡀⠘⠉⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⡀⠙⠛⠙⠋⡀⣾⣿⣿⣿⣿⣿⣿⣿⡇⡟⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡗⠁⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠙⢿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠙⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢟⠋⡉⣈⣤⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠐⢺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠠⠴⣯⣭⣽⣾⡿⠗⣾⠿⠛⠹⠥⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⣿⠀⢠⣿⡏⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⢠⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⡟⠀⣿⣿⠃⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡿⠁⣰⣿⠇⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⠃⢠⣿⡟⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡏⠀⣼⡿⠁⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⢰⣿⠃⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⣿⠇⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⡙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⣀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣿⣿⣿⣿⡿⠌⠻⣦⠙⢿⣿⣿⣿⢻⣿⣿⣗⠀⠀⠹⡀⠀⠀⢀⢠⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⢯⠃⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠆⠈⠻⣿⣿⠘⣿⠏⢸⠀⠀⠀⣷⣶⣶⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⠃⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣶⡎⠂⢀⢸⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⠏⠘⠀⣀⡴⠂⠡⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣰⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⠀⠀⢻⣿⣿⣶⣶⣤⣀⡀⠀⢻⣿⠓⠀⣼⢸⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡏⠀⢰⡿⠋⡠⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣧⣿⣿⢿⣻⣿⣯⣤⣤⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣦⢸⡟⠀⢤⡟⢸⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⡟⠀⠀⣨⣾⣊⣴⣾⡆⠸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⠃⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⡁⠀⠀⢰⣿⣿⣿⣿⣿⣄⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⠀⠀⠀⠿⣛⣩⣥⣶⣶⣦⡀⠙⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⣸⣿⣿⡿⠛⠁⠀⠀⠀⠘⠟⠻⣿⣿⣿⣽⣃⠀⡈⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⠋⠀⢰⣿⡿⠏⠁⠀⠀⠀⠀⠀⣀⣈⠙⢻⣟⡟⣛⢯⠀⠈⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⢀⣤⣶⣾⣿⣦⣀⣰⣤⣶⣶⣤⣿⢿⣶⣴⡶⡄⢸⣿⣷⣤⣻⡞⠦⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣺⡻⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣛⣋⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⡹⣿⣮⠻⠍⠣⠈⠿⡟⠘⢿⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠨⣿⣿⣿⣿⣿⣿⣯⣧⣿⣿⣿⠿⣡⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠃⢹⣿⣿⣿⢿⣿⣿⣿⠻⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣭⣿⣻⠿⠿⠟⠛⠋⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣭⣭⣥⣤⣶⣾⣿⣿⣿⠋⢰⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⠟⣿⠀⣠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣏⠿⢱⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣸⡛⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣫⡵⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠈⠿⠿⠿⠻⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣀⠹⢿⣿⣿⣿⣿⣿⣿⡀⠀⠛⢻⣒⣺⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⡛⠈⠉⠉⠉⠉⠉⢛⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠙⠿⣿⣿⣿⣿⣿⣳⢐⡓⠒⠛⠻⢣⠟⠣⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⣿⡀⠀⠀⡀⣀⣤⣾⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠉⠩⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⣿⡄⠀⠀⠉⠉⣽⣿⣿⣿⡟⠉⠙⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠟⠋⠅⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⡇⠀⣿⡇⠀⠀⠒⠊⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⡇⠀⣿⣷⣦⣤⣀⣠⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⠿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠒⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⣴⣴⣮⣿⣶⠒⢘⣿⣤⣽⡷⡦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣟⠏⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠊⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠂⠂⠀⠀⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⢿⣛⠛⠀⠀⠀⠀⠀⣠⠔⣰⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡆⢭⠟⠛⠁⠉⠀⠀⠀⠀⠀⠀⣾⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠇⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡇⢲⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠉⠉⠹⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 450 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/ffii-on-pl-holdings-upc/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/ffii-on-pl-holdings-upc/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ FFII:_In_PL_Holdings,_European_Court_of_Justice_Confirms_EU_Law_Cannot_be Outsourced_to_International_Courts_Like_Unified_Patent_Court_(UPC)⠀✐ Posted in Europe, Law, Patents at 7:05 pm by Guest Editorial Team By Benjamin HENRION, originally_posted_February_15,_2022 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇CJEU⦈_ Brussels, 17th Feb 2022 — The European Court of Justice has confirmed that EU law cannot be outsourced to international courts in its “PL Holdings sarl Vs Poland” decision. It is problematic for the architecture of the Unified Patent Court (UPC), which is an international court outside of the judicial system of the European Union, despite the claims of its supporters. The European Court of Justice (CJEU) has recalled in PL Holdings that Member States cannot remove disputes from the judicial system of the EU which deal with EU law: Lastly, it follows both from the judgment in Achmea, and from the principles of the primacy of EU law and of sincere cooperation, not only that theMember States cannot undertake to remove from the judicial system of the European Union disputes which may concern the application and interpretation of EU law […]. — Court of Justice of the European Union, Press Release No 190/21, Luxembourg, 26 October 2021, Judgment in Case C-109/20, PL Holdings, https://curia.europa.eu/jcms/upload/docs/application/pdf/2021-10/ cp210190en.pdf Since EU law covering patents is the Biotech directive and the Enforcement directive (IPRED), the interpretation of EU law is removed from the judicial system of the European Union, which is composed of the CJEU and the National Courts. The PL Holdings decision follow the same line of thought as the Achmea decision, where the European Court of Justice dissolved intra-EU investment courts (ISDS). In its Achmea decision (2018), the CJEU recalled the same functional link principle with the National Courts, as in Miles (2011): However, the arbitral tribunal at issue in the main proceedings is not such a court common to a number of Member States, comparable to the Benelux Court of Justice. Whereas the Benelux Court has the task of ensuring that the legal rules common to the three Benelux States are applied uniformly, and the procedure before it is a step in the proceedings before the national courts leading to definitive interpretations of common Benelux legal rules, the arbitral tribunal at issue in the main proceedings does not have any such links with the judicial systems of the Member States (see, to that effect, judgment of 14 June 2011, Miles and Others, C‑196/09, EU:C:2011:388, paragraph 41). — CJEU’s Case Case C-284/16, Achmea, https://eur-lex.europa.eu/legal- content/EN/TXT/?uri=CELEX%3A62016CJ0284&qid=1639573183575 Supporters of the UPC keep claiming it will be a Court Common to the Member States: The Unified Patent Court (UPC) will be a court common to the Contracting Member States and thus part of their judicial system. — Unified Patent Court website, About page, https://www.unified- patent-court.org/about If the Unified Patent Court is really part of their judicial system, why does the staff of the court need diplomatic immunity via the Protocol on Privileges and Immunities (PPI) of the Unified Patent Court? The European Court of Justice has allowed the Benelux Court of Justice to be part of the judicial system of the European Union, because it has a dialogue with National Courts, via a system of prejudicial questions. The UPC does not have any dialogue with the National Courts, it simply replaces them. The European Court of Justice is very much attached to the concept of Autonomy of EU law, which is in danger each time an international court outside of the judicial system of the European Union is allowed to interpret EU law. Member States which are no signatory of the UPC (because it is a super too- expensive court for SMEs) like Poland, Hungary, Spain or Czech Republic should use Art259 TFEU to ask the question to the European Court of Justice whether this construction is compatible with the architecture of the European Union: A Member State which considers that another Member State has failed to fulfil an obligation under the Treaties may bring the matter before the Court of Justice of the European Union. — Article 259 TFEU, EUR-Lex https://eur-lex.europa.eu/legal-content/ EN/TXT/?uri=CELEX%3A12016E259 § Links⠀➾ * Enforcement directive (IPRED): https://en.wikipedia.org/wiki/ Enforcement_Directive * Biotech directive: https://en.wikipedia.org/wiki/ Directive_on_the_legal_protection_of_biotechnological_inventions * CJEU judgment on ‘PL Holdings’, Press release No 190/21, 26 October 2021, Case C-109/20: https://curia.europa.eu/jcms/upload/docs/application/pdf/ 2021-10/cp210190en.pdf * Protocol on Privileges and Immunities (PPI) of the Unified Patent Court: https://www.unified-patent-court.org/sites/default/files/ ppi_final_ii_en_clean.pdf * FFII: Unified Patent Court is a fake Common Court and violates CJEU’s jurisprudence of the last 10 years, will explode at launch, says Pr Jaeger https://ffii.org/unified-patent-court-wont-survive-a-legal- challenge-at-the-european-court-of-justice-says-dr-thomas-jaeger/ * Wikimedia Commons: Palais de la Cour de Justice CJEU, July 2021, Sign and Towers B and C https://commons.wikimedia.org/wiki/File: Palais_de_la_Cour_de_Justice_CJEU_July_2021_Sign_and_Towers_B_and_C.jpg ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⠶⠂⢠⣦⢿⣌⣧⣿⡿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣇⣻⣫⣿⣶⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠖⠀⣸⡻⣯⣿⣞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣻⣯⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢤⠀⢀⣟⣿⣝⣿⡟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣽⣿⡆⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⡀⠀⢸⢿⣮⠿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢇⣿⢻⣿⣭⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢉⠁⠀⢻⣷⡻⢷⡾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣭⡏⣾⣿⣿⣿⢸⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠚⠚⠀⠀⣷⡈⠣⣞⠻⢞⢻⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⢿⢿⣻⣼⣭⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⠶⠶⠆⠀⢰⡈⠻⢠⡙⠧⡛⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⡤⡤⠀⠀⡈⠻⡆⡘⢷⡄⠻⡞⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠘⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⠁⠀⠀⢻⣦⠀⢿⣦⠙⣧⡁⢿⡻⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠀⠀⣴⣤⡙⢸⣦⡙⢴⣌⠻⣾⢻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠏⠔⠐⠒⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣠⣠⢰⢶⠆⠀⢠⡀⠙⠇⣄⡙⢇⣦⡙⢷⡾⣵⡭⢧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢱⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⢀⠀⠀⡼⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⡈⡀⠀⠀⠘⠿⣶⢀⠙⢿⢠⡙⠇⣍⠋⣦⡑⣦⣸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠚⠰⣀⣀⣀⣀⡴⠁⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠸⠻⠻⠿⠇⠀⠠⣷⣄⡀⠘⢷⡄⡘⢿⢠⡙⢷⣌⡿⣾⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣠⠀⠀⠠⡀⢆⠆⠢⠠⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⣄⡄⡄⡤⠀⠀⣀⠈⠛⢁⣦⣄⠁⢿⡦⣈⡻⣮⡻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡂⢤⣀⠀⣰⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠻⢿⡆⢀⠉⠻⣰⣦⡁⠻⡗⣜⢿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⢠⣆⣆⡞⡾⠀⠀⣰⣤⣀⠁⠻⢿⡆⣄⠙⠸⣶⢄⠟⢷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⣠⠀⡠⢠⠀⠂⠀⣴⡀⡡⠉⠃⠤⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠛⠿⢰⣦⣄⠀⠻⠟⣦⣌⠘⢷⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠈⠈⠁⠀⠀⣀⠀⠤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿ ⠀⠀⠀⠰⠧⠏⠟⠿⠀⠀⢸⣷⣦⡄⡈⠙⠋⢼⣶⢄⡉⠛⢿⣦⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠠⠀⠀⠘⠀⠘⠀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⡀⠉⠙⠠⢿⣷⢂⣄⡈⠘⠿⣧⣤⣊⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣴⡂⢢⠲⢰⠄⠄⡦⣼⢰⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠀⠀⠸⠧⠏⠟⠿⠀⠀⠰⣿⣷⡆⣠⣀⡈⠘⠻⠏⣶⣦⣴⣫⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⡀⣀⣀⢀⠀⠀⠀⣀⡀⠉⠁⠛⠿⠇⣶⣶⢥⣅⣩⢟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ䷩ 𝚕𝚒𝚗𝚎 631 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/gemini-capsules-on-the-internet/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/gemini-capsules-on-the-internet/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ List_of_Currently_Active_Gemini_Capsules_on_the_Internet⠀✐ Posted in Site_News at 7:21 pm by Dr. Roy Schestowitz Summary: The list of known (to Lupa) Gemini capsules continues_to_grow; it grew from 519 in February 2021 to 1,724 in February 2022 * 000000.flounder.online * 0gitnick.flounder.online * 0×1.net * 0×735.com * 0×80.org * 0xbad.flounder.online * 100sexts.flounder.online * 100words.flounder.online * 108mhz.flounder.online * 1436.ninja * 158.nu * 202x.moe * 2mas.smol.pub * 2pie.flounder.online * 3baid.flounder.online * 68k.myfirewall.org * 7-ph.com * 725.be * 7irb.tk * 80h.dev * 85-harvest.flounder.online * 9p.sdf.org * 9til.de * a.flounder.online * a1000duck.flounder.online * aaoth.xyz * abildgaard.com * acdtv.hopto.org * acdw.net * acesoren.cities.yesterweb.org * acidic.website * 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alvawang.flounder.online * alvin.flounder.online * alvin.paiges.net * amadeus.flounder.online * amanharwara.flounder.online * amdg.flounder.online * amer.pollux.casa * amethyst.cities.yesterweb.org * amiga5000.flounder.online * amigadu.de * amok.flounder.online * amomentzine.flounder.online * amplifibeats.pollux.casa * amvc.mx * anachronauts.club * and3rson.flounder.online * andinesia.flounder.online * andreafeletto.com * andygrn.co.uk * anime.flounder.online * anjune.lol * anniez1995.flounder.online * anorlondo.net * ansi.hrtk.in * antimass.flounder.online * antiphasis.flounder.online * antonio.e-worm.club * antonio.flounder.online * aoalmeida.com * aoeu.cities.yesterweb.org * aosync.me * aperalesf.flounder.online * aphrack.org * apintandaparma.club * appl.garden * aprates.dev * archipielago.uno * archiwistka.blog * armen138.flounder.online * armitage.flounder.online * arok.xyz * artur.gadziev.online * arydev.flounder.online * ascendinganthem.xyz * ascii.mozz.us * ascii.mozz.us:7070 * asciibene.flounder.online * asciinema.hrtk.in * ashaslan.flounder.online * aslowcab.flounder.online * asp.flounder.online * astrobotany.mozz.us * astroglitch.cities.yesterweb.org * astrognome.smol.pub * ataraxia.flounder.online * atlantis.luxe * atyh.cc * augers.srht.site * auken.flounder.online * auragem.space * autione.srht.site * auzziejay.cities.yesterweb.org * avalos.me * avfig.com * avocadosh.xyz * ax.flounder.online * axiomatika.flounder.online * axionfield.space * axolotl.flounder.online * azq.geminet.org * babiak.duckdns.org * baconicsynergy.flounder.online * bad-gateway.smol.pub * bakertribe.co.uk * bartender.midnight.pub * bartf1969.flounder.online * bbs.archaicbinary.net * bbs.ec * bcalderon.io * bearforceone.net * bebomuchocafe.flounder.online * beer.smol.pub * bel.flounder.online * benaaron.dev * benburwell.com * bencollver.cities.yesterweb.org * benj.smol.pub * bentsai.smol.pub * beta.lyk.so * beucismis.flounder.online * beyondneolithic.life * bi-rabittoh.flounder.online * billy.flounder.online * binarycat.flounder.online * binarythicket.xyz * birabittoh.smol.pub * bitdweller.flounder.online * bitshift.tokeniser.uk * bjornwestergard.com * bjw.flounder.online * bl4kers.flounder.online * blekksprut.net * blitter.com * bloatedloaf.flounder.online * blog.datapulp.de * blog.dumpr.org * blog.emisocks.com * blog.locrian.zone * blog.schmidhuberj.de * blube.club * bobignou.red * bobpelle.cities.yesterweb.org * bogart.flounder.online * bogwonch.net * bogwonch.smol.pub * bonehead.flounder.online * booksin.space * bootes.me * boss.flounder.online * botond.online * bouncepaw.flounder.online * brandontaylor2021.flounder.online * breadpunk.club * brewed.midnight.pub * brewed.smol.pub * brightblue.midnight.pub * brotfrau.flounder.online * bucareli.online * buetow.org * bugrother.flounder.online * bulletpr00f.host * bvnf.space * bwog-notes.chagratt.site * byrontakeda.flounder.online * byzoni.org * c0d3sh4p3r.flounder.online * c3po.aljadra.xyz * c3po.flounder.online * 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gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-170222.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmSARxzqsC4vGnHiUdAJ9Kne4qvG7nV2t9FCH7XejsbaWE #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmZyPf9PJ6yxMgQdnEGREYwuvY39FKUQjHNzdAjGTTaZ1N (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  QmUK84FkECET9k1THkpmWWskjhC4mnuFhyonYkDumEjy6F social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmX47y6dgiUFNnHbnmnGiRPmAhzJ6zKt5YC8r2XSNVJ5zL social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmPpMTmoTXgLrKuQQZbBWQTv8may5UTVuTwd8fLzqzQ1Lo #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmepFekuNjdsFftoQWC3rksg4BCQ3FtdU7uVX8gPJ5Rzfv (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmcjzL6f3MgiWmV4wPbaV8SK1gpMKNAuY752oF9knSZNQx #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmeinUYtxXyowyK2uXT567Vm1BbcL61cQ8Na5MFnE3m2bq (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmPgCJca3XFthf3S9xSXFzx2JdpEDjUZ3HPfAnGbLWi5kr ䷩ 𝚕𝚒𝚗𝚎 2506 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/linux-foundation-board-2022/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/linux-foundation-board-2022/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Linux_Foundation_Board_in_2022:_86%_Corporate_and_81%_Proprietary_Software Companies⠀✐ Posted in Deception, Free/Libre_Software, GNU/Linux, Kernel at 7:21 am by Dr. Roy Schestowitz It has only been getting worse over time 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Foundation's_board_in_2022⦈_ Summary: The Linux_Foundation has become just another phony apparatus like the Gates_Foundation and it cannot represent Linux, instead it_punishes_the_founder of_Linux; Still no update_or_IRS_filing_disclosed_since_the_2018_report (4 years ago; screenshot below is minutes old) 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇IRS_Linux_Foundation_status⦈_ 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⣿⣿⠶⠶⠶⠾⠰⠾⠾⠶⠶⠶⠿⠷⠶⠶⠿⠶⠶⠷⠶⠶⠷⠶⠷⠿⠾⠶⠶⠿⠦⠷⠾⠶⠾⠶⠾⠤⠿⠶⠷⠶⠷⠶⠿⠷⠶⠷⠶⠦⠾⠷⠾⠶⠾⠶⠾⠿⠶⠿⠷⠷⠼⠷⠶⠷⠶⠷⠶⠿⠿⠾⠧⠿⠶⠶⠿⠿ ⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣀⣉⣩⣩⣉⣅⣉⣉⣉⣉⣉⣹⢀⣩⣉⠉⣉⡁⣏⣡⣡⣉⣭⣝⣹⣈⣉⣹⣉⣨⣘⣀⣊⣏⣁⣁⣏⣄⣼⣉⣍⣁⣁⣳⣾⣍⣉⣋⣍⣉⣁⣈⣉⣏⣉⣉⣽⣁⣉⣍⣀⣘⣉⢉⣏⣈⣉⣭⣹⣉⣉⣉⣉⣿⣉⣉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⠝⣿⣿⡍⠉⠩⡍⠉⠉⢹⠉⢉⠉⢙⢉⠉⠉⠉⡋⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⡙⣿⣿⡍⠛⠛⡉⠛⠛⢻⠙⠙⠩⢹⢉⠛⠛⠛⠋⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭ ⣿⣿⣿⣿⡻⣿⣿⡛⠻⠿⠛⠻⠻⢿⠛⠛⠻⠻⠛⠿⠻⠛⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣵⣿⣿⣷⣶⣶⣷⣶⣶⣾⣶⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠿⣿⣿⠛⠿⠿⠻⠿⠿⢿⠻⠻⠿⢻⠛⠿⠿⠿⡿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣵⣿⣿⣷⣶⣶⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣥⣩⣨⣭⣗⣭⣬⣌⣭⣄⣉⣭⣰⣩⣮⣉⣌⣄⣨⣅⣺⣠⣬⣤⣨⣅⣭⣅⣩⣭⣀⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 2711 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/linux-hostile-foundation/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/linux-hostile-foundation/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Rest_Assured_the_Linux_Foundation_Does_Not_Really_Speak_for_Linux_(Not Anymore)⠀✐ Posted in Free/Libre_Software, GNU/Linux, Kernel, OSDL at 11:23 am by Dr. Roy Schestowitz Video_download_link | md5sum d6256f67dc837bd44b75ac7d9d0342cf Not the Voice of Linux Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/who-bosses-lf.webm Summary: The employer of Linus_Torvalds, who remains_the_trademark_holder_of "Linux", is clearly aligned against_the_goals_of_Linux_as_a_project and as a community THE Linux_Foundation, as noted in the above video, came about after OSDL had blown up. The Linux Foundation claims to be older than it really is (the University of Manchester does the same thing for that matter, cherry-picking historical dates) and within only a few years it lost its direction. Today, in 2022, the_Linux_Foundation's_Board_of_Directors_is_almost_90%_corporate and more than 80% proprietary companies (mostly ‘suits’ who don’t even use GNU/ Linux). Judging by the way things change every year, the Board might be over 90% corporate some time soon (maybe as soon as next year) because they literally sell seats on the Board. They even market it that way (we showed evidence of this before, based on their own words). You pay for a certain membership tier and in exchange you get to exercise control over Linux and more. “It’s indisputable at this point that it’s just a front group or a shell of very affluent companies, some of them not even American.”It’s quite frankly a miracle that the IRS still lets this thing go on without having to pay any taxes. It’s indisputable at this point that it’s just a front group or a shell of very affluent companies, some of them not even American. I’ve said a lot more in the video above as I commented, one by one, on the 26 members of the Linux_Foundation’s_Board_of_Directors. Even outside the Board, in the management team of the Linux Foundation, there_are_prominent Microsofters. There is no simple soluton or quick ‘fix’ to this sordid mess. The Linux Foundation buying positive media coverage about the Linux Foundation (in essense corrupting the media) leads to a different kind of backlash and other sorts of scandals, as we’ve noted here before. They also run_afoul_of_rules, which means they can get banned. █ ䷩ 𝚕𝚒𝚗𝚎 2780 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/lxer-not-reachable/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/lxer-not-reachable/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ LXer_Not_Reachable_Since_February_16th_(Updated)⠀✐ Posted in Free/Libre_Software, GNU/Linux at 2:42 am by Dr. Roy Schestowitz Summary: As of this time, the cause remains a mystery, there is only speculation at this point and no visible answers 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LXer_issue⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LXer_out⦈_ Update: The culprit now becomes more obvious. 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇wmkt.net_expired⦈_ ⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ 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⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 2967 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/megaphone-for-campinos/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/megaphone-for-campinos/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Megaphone_of_António_Campinos⠀✐ Posted in Europe, Patents at 2:45 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IP address not found. Please try again.⦈ Summary: EPO President António_Campinos helped by a little rigging from Benoît Battistelli-bribed ‘media’ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢩⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣣⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠮⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣟⣓⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠈⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠀⠛⠀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠄⠀⠂⠈⠁⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡟⢰⣧⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠿⠟⠛⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠠⠀⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⡍⠉⠈⠭⠭⠜⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡄⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⢾⡿⠏⢿⡽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠀⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣭⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⡿⠦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣩⠙⠈⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠙⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠒⠉⠐⠛⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁⠄⠀⠂⠈⠅⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡟⢰⣧⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⣻⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠁⠂⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⡍⠉⠈⠭⠭⠌⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡄⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⠾⡿⠏⠿⡽⠧⠿⠿⢇⠷⠻⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠿⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣇⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠁⠾⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⡍⠉⠈⠩⠍⠼⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⠧⠇⠧⠾⠿⠏⢿⠽⠧⠿⠿⢇⠷⠻⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⡲⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣹⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠐⠟⣀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢹⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣻⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠯⣍⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣓⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠓⠇⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢯⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢩⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢨⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠚⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠕⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⡞⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣟⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠂⠉⠐⠿⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⡁⠀⠐⠂⠈⠥⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⣉⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⡍⠉⠈⠩⠍⠴⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠈⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⠧⠇⠧⠾⡿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠓⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠰⣿⣷⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠂⠉⠐⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠁⠀⠐⠀⠈⠅⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣾⢸⠀⠀⡏⢙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠹⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠠⠄⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⠍⠉⠈⠭⠭⠴⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡞⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⢾⡿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⢹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣟⣓⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢇⠄⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣄⠘⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⢿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠗⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠁⠀⠐⠀⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣾⢸⠀⠀⡏⢙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠀⠠⠄⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠔⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣷⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⠧⠇⠧⠾⡿⠏⢿⠽⠷⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⡿⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣷⣿⣿⣿⣷⣿⣴⣶⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣯⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢠⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⠍⠉⠈⠭⠭⠴⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⠾⠿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣋⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠛⠛⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⢰⣿⣿⡗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢀⠸⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠒⠉⠐⠿⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⣿⣿⣭⣭⣿⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⡼⢿⣿⣿⣿⣿⣿⣿⣿⣻⣓⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠟⠈⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⢠⣿⣦⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⢿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣿⣿⣿⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣾⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠐⠟⡀⡀⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡁⠀⠐⠂⠈⠅⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⢙⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡄⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠭⠭⠄⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣷⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⠾⡿⠏⢿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⡿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⡄⠛⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠸⠁⠀⢀⠀⠀⠀⠐⣿⣿⠇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣾⣷⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡿⣻⣿⣿⣿⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣹⢿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠐⠗⠀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡁⠄⠀⠂⠈⠅⠈⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡷⢿⣸⡇⢀⣸⡃⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠌⠡⠍⠉⠈⠩⠭⠄⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠧⠇⠧⢾⡿⠏⢿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⣰⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠸⠁⠀⢀⠀⠀⠀⠀⢨⣿⠿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢯⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⢈⢉⣼⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⣿⣿⣹⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠟⡀⣀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⡁⠄⠀⠂⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢻⣶⡏⠙⢺⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠌⠥⠍⠉⠈⠩⠭⠤⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⡲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠷⠇⠧⠾⡿⠏⣿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢩⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣷⣮⣽⣿⣿⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠿⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣷⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣯⡟⣹⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠭⠥⠌⠥⠍⠉⠈⠩⠭⠤⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⠾⡿⠏⣿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢩⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣿⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢟⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢿⡿⣿⠻⣿⣿⣿⣿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣷⣮⣽⣿⣿⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠽⠿⠿⠛⠭⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣯⡟⣹⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠃⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡇⡀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⣍⣝⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⢀⠸⠃⠀⢀⠀⠀⠀⠘⠓⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢿⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢯⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⠚⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⣹⣿⣿⣽⣯⣮⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠐⠉⠐⠟⡀⣤⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠆⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢩⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣿⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢿⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣷⣮⣽⣿⣿⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠽⠿⠿⠛⠩⠝⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣯⡟⣹⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⣽⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠸⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⡘⠃⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣿⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⢀⠸⠃⠀⢀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣯⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢿⣹⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⣯⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣽⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣹⣿⣿⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠒⠉⠐⠟⣀⣠⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠞⠀⡁⠄⠐⠂⠉⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⣶⡏⠹⢺⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⢹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠭⠥⠬⠥⠍⠉⠈⠭⠭⠤⠬⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⣲⡞⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⣿⡽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠲⣶⠀⠰⠄⠠⠰⠖⠆⠀⠀⠠⠀⠀⠀⠂⠀⠂⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢩⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⣿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⣿⢻⡟⢿⣿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣾⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣿⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⢀⠸⠃⠀⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣹⣿⣿⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠟⡀⣠⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠞⠀⡁⠄⠐⠂⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⢹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠌⠥⠍⠍⠈⠩⠭⠤⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣷⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⢿⡽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⢾⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣾⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠰⠃⠀⢀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⣀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⡁⠄⠐⠂⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡏⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡇⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠌⠥⠍⠉⠈⠩⠭⠤⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⢿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠤⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣶⣦⣶⡲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⠾⡿⠏⢿⡽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⡟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣯⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⢹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣁⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣍⡛⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣤⣸⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣟⣿⣿⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠃⠀⢀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠈⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⢟⡿⣹⣇⣏⣽⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⠀⣀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢩⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢒⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣾⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⢸⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣟⣿⣿⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⢟⡿⣹⣇⣟⣽⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣥⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣜⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣹⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣣⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠚⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢿⣟⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠸⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣏⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠉⠀⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁⠄⠀⠆⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣧⠀⡟⢹⢶⡏⠹⢲⡟⣻⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⡍⠍⠈⠩⠭⠄⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⡲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⠾⠿⠏⢿⠽⠧⠿⠿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢿⣏⣿⣻⣉⣾⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⡁⠄⠀⠆⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡏⢹⢶⡏⠙⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣾⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⢸⠀⣿⢸⠀⠀⡇⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠀⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠄⠄⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣖⡆⡖⢶⣶⣦⣶⣲⡖⣶⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⠿⠏⣿⠽⠧⠿⠿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣽⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣾⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣭⡟⢹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⣸⢿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢿⠿⠛⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⢠⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣷⣽⣿⣿⣾⣿⣿⡿⣿⣿⣟⣟⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣲⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣹⢿⣟⣽⣯⣾⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⡁⠄⠀⠆⠈⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⠙⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠀⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠄⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⠿⠏⡿⠽⠧⠿⢿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠁⣿⣟⣻⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣬⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⠛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡏⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣻⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣷⣿⣿⣷⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⢿⣿⣭⡟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣼⢽⡌⡷⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠡⠤⠥⠥⠬⠥⠍⠉⠈⠩⠭⠠⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡞⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣖⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⠿⠏⡿⠽⠧⠿⢿⢇⠷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢫⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣾⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣷⣮⣽⣟⣻⣯⣽⣿⣿⣿⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⠟⣹⣿⢿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⡀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⢻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⠁⠀⢀⠀⠀⣣⣾⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣾⣷⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡽⣷⣯⣷⣳⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣹⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣟⣿⠛⣿⢹⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣼⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣾⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣼⣧⣾⣧⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⠧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣍⣽⣛⣏⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣾⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣽⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠨⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢿⠄⢀⣷⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⢻⡿⣴⣿⣿⣿⣿⡟⣿⢋⣿⠛⣿⢡⣿⢛⣿⠉⣿⣟⣿⣿⣻⡿⢹⣯⣹⢻⣿⣝⣿⣿⣿⣿⠛⣿⢻⣿⠋⣿⢩⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣶⣿⣼⣿⣾⣿⣼⣿⣾⣿⣶⣿⣾⣿⣿⣴⣿⣷⣼⣿⣶⣼⣿⣿⣿⣿⣿⣴⣿⣼⣿⣼⣿⣼⣯⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⢚⣿⠛⣿⢛⣿⢻⣿⠛⣿⠟⣿⢻⣿⢳⣿⣼⣿⣿⣿⡿⣿⣇⣾⠇⣿⠏⣿⢛⣿⢻⡿⢻⡟⣿⣟⡻⢻⡟⣻⣿⣿⣿⣿⣗⣟⣿⢟⡿⣿⠻⣿⣿⣿⡿⢻⡟⢿⡿⢻⡿⣻⡟⣿⠟⣿⡟⢻⡟⢻⣿⣿⣿⣿⣿ ⣿⣿⣧⣾⣿⣴⣿⣼⣯⣼⣯⣼⣿⣼⣿⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣼⣿⣭⣷⣾⣧⣾⣵⣮⣽⣟⣿⣯⣽⣿⣿⣷⣿⣼⣿⣿⣿⣷⢿⣶⣿⣿⣿⣧⣾⣧⡻⡧⣼⣇⣿⣤⣿⣤⣿⣤⣿⣧⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣝⡟⡿⠯⠝⠻⠿⠛⠩⠍⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣿⣿⣷⣿⣴⣷⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣭⡟⣹⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣭⣿⣛⣏⣥⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡿⣿⢿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢉⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣏⣿⣿⣿⣾⣽⣫⣿⣿⣿⣿⡿⢿⣿⢿⢿⢟⣿⣿⡿⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⡟⣿⢻⣏⣿⣻⣉⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣻⣟⣿⣿⣫⣿⣧⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⢠⢀⠨⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⡿⣏⢯⣱⣽⣾⣵⣾⣷⣷⣿⣿⣿⣿⣿⣿⣻⢻⢭⣿⣿⣷⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⡿⣻⢟⡿⣹⣇⣟⣽⣷⣾⣿⣿⣾⣿⣿⡿⣿⣿⣿⣽⣶⣿⣱⣥⣿⣽⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠷⠶⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢟⣻⣿⣿⣟⡿⣷⣯⣷⣱⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠈⢆⣀⠀⣿⡆⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣹⣿⣟⣽⣯⣮⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠉⠐⠛⡀⣄⠀⠀⠀⡈⠋⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟⠀⡁⢄⠀⠆⠉⠅⠘⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣧⣸⡗⢰⣷⠀⡟⢹⢶⡏⠹⢲⡟⣿⠀⠀⣿⢙⡇⣼⡆⢸⠀⣿⢸⠀⠀⡏⢹⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣧⣾⢽⡌⡿⢿⣸⡇⢀⣸⡇⣿⠀⠀⣿⠋⢀⡯⣷⣸⠀⣿⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠄⠠⠀⠬⠥⠤⠭⠥⠤⠥⠥⠬⠥⠭⠉⠈⠩⠭⠤⠤⠁⠀⠈⠀⠈⠈⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⣶⡆⡖⢶⣶⣦⣶⣲⡖⣾⣷⡆⡶⣴⡆⢰⣴⣶⣲⣰⠀⣦⣶⢲⣶⢲⡒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠿⠇⠧⢾⡿⠏⣿⠽⠯⠿⢿⢇⡷⠿⠇⠸⠹⠧⠼⠿⠄⠏⠿⠼⠿⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠲⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 4134 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/meme-a-social-democracy-where-every-vote-is-for-sale/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/meme-a-social-democracy-where-every-vote-is-for-sale/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_A_‘Social_Democracy’_Where_Every_Vote_is_for_Sale⠀✐ Posted in Europe, Patents at 7:41 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Will you vote for Campinos? Make me!⦈ Summary: António_Campinos might need to embark on another journey to the “eastern front” to secure_the_"crown" of EPO (maybe EPO ‘cooperation’ bribe money will help) 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Emruli_and_António_Campinos⦈_ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠉⠻⡿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣕⣤⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠃⠉⡒⣿⣮⢟⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡤⠀⠀⠀⠡⠔⢀⠅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠂⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⡐⢀⠀⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠐⡀⠀⠀⠀⠀⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠁⢈⠀⠀⠘⢏⡻⠉⠁ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⡀⡊⠀⠀⠀⠐⢁⣉⡀⠀⠀⠉⡈⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠼⢓⣠⣿⣿⡿⢮⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠂⠀⢐⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣆⢀⢀⣠⢪⢳⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢿⡈⠌⠉⢀⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⡛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡆⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢬⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⣿⣿⣿⣯⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⠙⡐⢸⣿⡟⢠⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠘⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⠿⣛⣻⣯⣭⣭⣿⣿⣿⣿⣯⣭⣥⣥⣛⠋⠠⠛⢛⣩⠐⡊⠀⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⡀⠀⢹⣷⢀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿ ⣿⣿⠊⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢉⣁⢍⠂⠀⠉⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉ ⣿⣿⠀⠈⠛⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣭⣔⡀⠀⠈⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣼⠐⠀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠀⣼⣿⣿⣻⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⣿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠒⠄⠀⠀⠀⢬ ⣿⣿⣿⣆⣀⡀⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣷⢘⣟⠋⡈⢂⠀⠀⠘⠉⣇⢻⣷⣄⣂⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⢻⣧⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⠻⠮⠞⠿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠨⢿⣿⣿⣿⣿⣷⣤⡄ ⣿⣿⣿⣿⣿⣿⡌⣟⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠻⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢨⢆⢶⠀⠐⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣌⢮⣛⣛⣛⣫⠜⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⣿⢣⣿⡟⣤⣤⣴⣴⣿⣿⣷⣿⣷⡶⠊⣿⣿⣿⣶⣝⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢄⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣧⣿⠉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠂⠀⠀⠀⢀⠐⠃⠀⠉⡄⠀⠅⠈⠁⠔⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢂⡀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠈⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢔⣤⣁⠀⠀⠀⠀⠀⠀⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⡠⠂⠉⠂⡟⣦⢇⠡⢸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣬⣿⣿⣿⠟⠁⠀⠀⠀⠀⠌⠀⠀⣴⠀⢉⡄⠀⠀⠀⠠⠐⢀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣾⣿⣿⣶⣿⣿⡞⠐⠳⠚⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⡁⠀⠀⢸⣿⣿⠿⢁⢙⣫⣿⠛⠉⢋⣑⠐⢀⠠⠀⠈⢀⣠⣶⢟⡙⣤⣄⡃⠐⡀⠀⠀⠀⠠⠐⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢈⡛⠉⠁ ⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣤⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠠⠀⣐⡀⠀⠀⠀⠀⠀⢀⣉⡀⠀⠀⠈⡈⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⠀⠀⠀⠄⠸⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⣿⡟⢤⣾⣿⣿⠯⣾⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣫⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣆⠀⢀⢠⢢⢠⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣽⣿⢫⡈⠌⠉⠁⠨⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣵⡀ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣅⣤⣴⣿⣿⣿⣿⠿⣩⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢭⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿ ⣿⣿⣷⠘⢿⣿⡿⡟⣶⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣏⠙⠀⢸⣿⠟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿⢿⣿⣟⣛⣛⣻⠿⠉⠃⠑⣿⡛⠠⠛⢹⣩⠐⡊⠀⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⡿⠿⣿⡟⠒⢀⣬⡈⠀⠀⢉⣁⢍⡂⠀⠁⣇⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢐⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉ ⣿⣿⠀⠀⠛⢿⣿⣿⡿⣫⣶⣿⣿⡿⣻⣿⣿⣟⣷⣦⡀⠙⠃⠀⢸⣿⣿⣦⠀⠘⢻⣭⣔⡀⠀⠨⣉⣷⣑⡇⣿⠁⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠐⡘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠠⣼⡟⣼⣿⣿⣿⣟⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⠸⢿⣿⣿⣷⠵⠒⠄⠁⠀⠀⠬ ⣿⣿⣿⣆⡀⣄⡔⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢚⣟⠋⡌⠂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣶⣤⡤⠀⠀ ⣿⣿⣿⣟⢿⣿⡇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⡀⠀⠀⡘⣯⣙⣏⠀⠈⠻⠦⠾⠿⠞⠀⠀⣠⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠊⠨⢿⣿⣿⣿⣿⣷⣤⡄ ⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⣟⣵⣿⣰⣗⠀⠨⣷⣌⣃⠞⠀⠰⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣼⣿⣿⡏⣤⣤⣴⣶⣿⣿⣷⣾⣷⣶⠞⣿⣿⣿⣶⣝⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡟⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣀⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿⢿⣿⣟⣛⣛⣻⠿⠛⠃⠑⣿⡋⠠⠛⢛⣉⠐⡊⠀⠹⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⡀⠀⢹⣷⢨⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿ ⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⡿⠿⣿⡟⠒⢀⣬⡈⠀⠀⢉⣁⢅⡂⠀⠈⣇⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⢈⢿⣿⣇⠀⠀⢸⣿⡇⠄⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠍ ⣿⣿⠀⠈⠛⣿⣿⣿⡿⣫⣶⣿⣿⡿⣻⣿⣿⣟⣷⣦⡀⠙⠃⠀⢸⣿⣿⣦⠀⠘⢿⣭⣴⡀⠀⠨⣉⣥⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⠀⠀⠀⡤⠻⠿⡀ ⣿⣿⡄⠀⠀⠠⣼⡟⣼⣿⣿⣿⡟⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠵⠒⠄⠁⠀⠀⠬ ⣿⣿⣿⣆⡀⣄⡄⣸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢚⣟⠋⡐⢂⠀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⣿⣿⡇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⡀⠀⠀⡘⣯⣙⣏⠀⠚⠻⠦⠟⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⠘⢫⠈⠨⢿⣿⣿⣿⣿⣷⣄⡄ ⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⣟⣵⣿⣠⣗⠀⠨⣷⣌⣛⠟⠀⠰⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢨⢆⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣴⣿⣿⡏⣤⣤⣴⣶⣿⣿⣷⣷⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠍⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡟⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢄⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣥⣿⠉⡁⠉⢉⣢⠀⢃⣀⣿⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⠀⠐⠃⠀⠉⡄⠈⠅⠈⠁⠴⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠈⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣄⣴⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⡠⠃⠋⡒⣿⣮⣟⠧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣤⣶⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠂⠀⣴⠀⢉⡤⠀⠀⠈⠡⠐⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⣿⣿⣿⣶⣿⣿⡟⡘⡻⠛⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠂⡈⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⠐⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠰⡀⠀⠀⠈⠡⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠂⠀⠀⠀⠀⠁⠌⠀⠀⠘⢏⡛⠉⠁ ⣿⣽⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠤⠀⣐⡀⡁⠀⠀⠀⠐⢀⣅⡀⢀⠀⠉⡈⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠼⢃⣠⣿⣿⡿⢮⣬⣿⣧⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠯⣽⣿⣿⣿⠟⠻⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⠀⢀⣠⢪⢹⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢯⡨⠌⠉⢑⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⡻⠿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀ ⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢹⣿⣿⡇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣫⣾⡑⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠠⠀⢀⢩⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⣿⣿⣿⢟⣿⡋⣼⣿⣿⣿⡟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣭⡙⠐⢸⣿⡟⢠⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠄⠀⠹⣿⣿⣿⡄⠀⠀⠘⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣩⠐⡎⠀⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠠⢹⣷⢨⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢳⣿⣿⣗⠍⠂⠀⢁⣇⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⣀⡀⠀⠠⠀⣠⠞⢹⣿⣿⠉ ⣿⣿⠂⠀⠛⢿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠘⣿⣿⣿⣭⣔⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠀⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⣼⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠷⠗⠄⠁⠀⠐⠬ ⣿⣿⣿⣆⣀⣄⡄⠈⣻⣷⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⣈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣶⣤⡄⠀⠀ ⣿⣿⣿⣟⢿⣿⣿⣷⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡦⠀⣴⣿⠃⠻⢦⠿⡿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⡊⠈⢿⣿⣿⣿⣿⣷⣤⡄ ⣿⣿⣿⣿⣿⣿⣿⣭⣽⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣭⣿⣿⣶⡿⠋⠨⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠗⡀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠍⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⣄⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢹⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣥⣿⡉⡁⠉⢩⣦⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣖⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⡟⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⢀⠐⠃⠀⠙⣄⠈⠅⠈⠃⠼⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣾⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠈⠈⠈⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣕⣴⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠁⢀⠀⡠⠃⠋⡒⣿⣮⣟⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣶⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡄⠀⠀⠈⠡⠐⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣷⣿⣿⣿⣶⣿⣿⡿⡘⡺⠚⢋⢉⠄⠀⠃⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣛⠐⢀⠠⠀⠀⢀⣠⣶⢿⡙⣼⣕⡋⠰⡀⠀⠀⠀⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠉⠀⠀⠀⠀⠐⠁⠈⠀⠀⠘⢏⡻⠉⠁ ⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⣐⣀⡋⠀⠀⠀⠀⢠⣉⡀⠀⠀⠉⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠼⢃⣠⣿⣿⡿⢦⣬⣿⣧⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡞⠂⠀⢐⡆⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⣂⢀⣠⢪⢳⣾⣿⣿⣿⣿⣿⣏⣩⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡨⠌⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⡈ ⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢹⣿⣿⡇⣰⣿⣅⣥⣶⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠈⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢫⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿ ⣿⣿⣷⠘⢿⣿⡿⣟⣶⡋⣼⣿⣿⣿⡟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⡙⠀⢸⣿⡟⢡⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠄⠀⠹⣿⣿⣿⡄⠀⠀⠘⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠀⡳⣀⡛⡉⠐⡊⠈⠹⡙⣿⣿⣿⣿⠏⣾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⡘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢳⣿⣿⣗⢍⠂⠀⠈⣆⡾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⣀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉ ⣿⣿⠂⠀⠛⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠘⣿⣿⣷⣭⣴⡀⠀⢩⣉⣷⣓⡇⣿⠁⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⣼⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⣿⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡷⠓⠄⠁⠁⠀⠬ ⣿⣿⣿⣆⡀⣀⡄⠈⣻⣷⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⣈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⣿⣿⣿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡦⠀⣴⣷⠃⠹⠦⠾⡿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⡈⠨⢿⣿⣿⣿⣿⣷⣤⡅ ⣿⣿⣿⣿⣿⣿⣿⣯⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣭⣿⣿⣶⡿⠋⠨⠨⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⣿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢈⢆⢶⠀⠐⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣷⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠍⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠠⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠸⣿⣿⣿⣿⢞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠋⠠⠛⢛⣭⠐⡎⠀⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⡀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⡟⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣁⢍⠂⠀⠁⣇⡾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⣀⡀⠀⠠⠄⣠⠞⢹⣿⣿⠍ ⣿⣿⠂⠀⠛⣿⢣⣿⣿⢧⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠘⢿⣭⣔⡀⠀⠨⣉⣧⣓⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⢀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣾⠐⢀⠈⠀⡀⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⢼⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⠇⠀⠐⠀⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢢⣔⠀⠀⣻⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠕⠄⠁⠀⠘⢤ ⣿⣿⣿⣆⣀⣠⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢾⣟⠋⣘⢂⠀⠀⠙⢉⣇⢻⣷⣄⣂⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⢻⣿⣴⣶⣶⣤⡤⠀⠀ ⣿⣿⣿⣟⢿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡺⠹⢦⠿⡿⠞⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢰⣶⠉⡙⢫⠈⠨⢿⣿⣿⣿⣿⣷⣤⡄ ⣿⣿⣿⣿⣾⣿⣿⡄⢿⣷⣂⠀⢵⣮⣋⣭⣿⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠲⠈⣴⣞⡃⠀⠴⠂⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢨⢆⢶⠀⢒⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⢷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣴⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠩⠭⠉⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠿⢿⣿⡿⢿⡿⣿⣿⣿⣹⣯⠀⢿⣿⣿⣿⣿⣿⣷⢸⣿⢿⣿⡷⣄⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡑⠉⢉⣢⠀⢋⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣾⣿⣿⣾⣿⠿⣟⣻⣯⣭⣭⣿⣿⣿⣿⣯⣭⣭⣥⣛⠛⠠⠛⢛⣍⠐⡊⠈⠹⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢉⣁⢅⡂⠀⠈⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡆⠂⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍ ⣿⣿⠀⠈⠛⢿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣭⣄⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠈⣼⣿⢿⣻⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣔⠀⠀⢻⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠓⠄⠀⠀⠐⠬ ⣿⣿⣿⣆⡀⡀⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣧⢸⣟⠋⡐⢂⠀⠀⠘⠉⣇⢻⣷⣄⣀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⢷⣧⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⡻⠮⠞⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠨⢿⣿⣿⣿⣿⣷⣤⡄ ⣿⣿⣿⣿⣿⣿⡎⣞⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠰⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢣⣿⡏⣤⣤⣤⣶⣿⣿⣷⣷⣷⣶⠞⣿⣿⣿⣶⣝⠉⠉⠩⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢼⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢾⣿⡷⢄⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠍⡑⠉⢉⣢⠀⢃⣀⣿⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣾⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠠⠛⢛⣩⠐⡊⠀⠙⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠠⣠⠉⠈⠀⠀⢉⣁⢍⡂⠀⠉⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠏⢹⣿⣿⠉ ⣿⣿⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣄⡀⠀⠈⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠀⠊⢙⣿⣿⣿⣄⠈⣿⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⡕⠕⠄⠁⠀⠀⢬ ⣿⣿⣿⣆⡀⣀⢄⣬⣷⣶⣶⣶⢖⣤⣭⣥⣤⣄⠀⠒⠾⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡘⢂⠀⠀⠘⠉⣇⢻⣷⣄⣀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠈ ⣿⣿⣿⣟⢿⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠘⠦⠞⠿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⡈⠈⢿⣿⣿⣿⣿⣷⣤⡄ ⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠪⠿⣿⡿⢟⡱⠠⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢰⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣿⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣿⣿⣟⣤⣶⣿⣿⣷⣷⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⠛⢻⣯⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠈⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡍⡁⠉⢉⣢⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣢⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣾⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠑⣿⡛⠢⠙⢛⣉⠐⡊⠀⠩⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠊⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢀⠠⣠⠉⠈⠀⠀⢉⣁⢍⡂⠀⠉⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠀⣐⡀⠀⠠⠂⣠⠎⢹⣿⣿⠍ ⣿⣿⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠈⢻⣭⣄⡀⠀⠈⣉⣵⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣾⠐⢀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠐⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠀⠊⢙⣿⣿⣿⣄⠈⣿⣿⣿⠇⠀⠐⠀⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠗⠄⠁⠁⠀⠬ ⣿⣿⣿⣆⡄⣄⢄⣬⣷⣶⣶⣶⢖⣤⣭⣥⣤⣄⠀⠲⠾⠃⠠⠇⢻⣿⣿⣿⣿⣷⡜⣟⠋⡌⢂⠀⠀⠘⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣶⣤⡄⠀⠈ ⣿⣿⣿⣟⢷⢱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠘⢦⠞⡿⠞⠀⠀⣠⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠊⠈⢿⣿⣿⣿⣿⣷⣤⡄ ⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣌⠪⠿⣿⡿⢟⡱⠠⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣇⠀⢋⢨⢇⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣮⣟⣿⡿⣿⣫⣆⣾⣧⣆⢀⣸⣿⣶⣾⣿⣟⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⢿⣿⣿⣿⣿⣾⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢾⣿⢙⢻⣯⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠍⡁⠉⢉⣢⠀⢃⣠⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠀⠀⠀⠐⠃⠂⠙⣄⠈⠅⠈⠁⠔⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣷⠊⠻⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣥⢀⠈⠀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⡠⠃⠉⡒⣿⣮⢟⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣬⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡄⠀⠀⠀⠡⠐⢀⠅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢂⢙⣫⣿⠛⠉⢛⣛⠀⢈⠀⠀⠀⢀⣠⣶⢟⡙⣤⣕⡋⠐⡀⠀⠀⠈⠠⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⡀⠀⠀⢀⠀⠁⠈⠀⠀⠘⢏⡛⠉⠁ ⣿⣽⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠤⠀⣐⡀⡋⠀⠀⠀⠐⢡⣍⡀⠀⠀⠉⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⡿⢦⣼⣿⣥⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣏⣀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣿⣿⢻⡨⠌⠉⢐⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⡛⡻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣷⡀ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⡀⠀⠀⠈⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⣿⣿⣿⣛⣮⡉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠟⠐⢸⣿⡟⢡⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠘⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⢿⣿⣟⣛⣛⣛⠿⠙⠃⠑⣿⡋⠠⠛⢛⣉⠐⡊⠈⠹⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⡿⠿⣿⡟⠒⢀⣭⡈⠀⠀⢉⣁⢅⡂⠀⠈⣇⠾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍ ⣿⣿⠀⠈⠛⣿⣿⣿⡿⣫⣶⣿⣿⡿⣻⣿⣿⣟⣷⣶⡀⠙⠃⠐⢸⣿⣿⣦⠀⠈⢿⣭⣄⡀⠀⠈⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⢀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠐⠀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⣬⡟⣼⣿⣿⣿⡟⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡷⠕⠄⠀⠁⠀⠬ ⣿⣿⣿⣆⡀⣀⡄⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠐⢾⣟⠋⡔⢂⠀⠀⠘⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⢳⣿⡇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⠀⠀⠀⡘⣯⣽⣋⠀⠙⡻⠦⠞⠿⠞⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢰⣶⠉⡘⠫⡈⠈⢿⣿⣿⣿⣿⣷⣤⡄ ⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⣷⣿⣻⡿⠿⣟⣷⣿⣰⣗⠀⠨⣷⣌⣛⠏⠀⠣⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⠐⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣼⣿⣿⡏⣤⣤⣤⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣢⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠂⠀⠁⠀⠀⠐⠃⠀⠙⡀⠈⠁⠈⠁⠤⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠛⣻⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠁⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⢳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡦⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠻⠋⠁⡀⠀⣅⣥⣥⢀⠈⠀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠃⠉⠒⣿⣮⢟⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠊⠀⣴⠈⢁⡄⠀⠀⠀⠡⠐⢀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢋⣓⠈⢀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠐⡀⠀⠀⠈⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⠉⡀⠀⠀⠀⠀⠁⠨⠀⠀⠘⢎⡛⠉⠁ ⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢿⣿⣿⣘⣿⣶⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⡀⡋⠀⠀⠀⠐⢁⣁⡂⠀⠀⠉⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢓⣠⣿⣿⣿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠂⠀⢀⡄⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣿⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⢀⢀⢠⢪⢱⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣋⣿⣿⢫⡨⠬⠉⢐⡈⠤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⡻⠿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢹⣿⣿⠇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢭⢻⣿⣿⣿⣿⣿⢿⣿⣿⠋⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⣿⣿⡿⢻⣷⡋⣼⣿⣿⣿⣟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⡙⠀⢸⣿⠟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠘⣧⡩⠁⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣁⠐⡊⠀⠱⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣦⡀⠹⠃⠀⢳⣿⣿⡗⢍⠂⠀⠈⣇⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠀⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉ ⣿⣿⠀⠈⠛⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣄⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠂⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠨⠀⡄⠻⠿⡀ ⣿⣿⡄⠐⠀⠨⣼⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠀⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢪⣔⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠕⠄⠀⠀⠘⠬ ⣿⣿⣿⣆⡄⣀⡄⢈⣹⣧⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢛⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⣗⣿⣿⣷⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣳⡇⣸⡦⠀⣰⣿⠃⠻⠦⠞⡿⠞⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢨⣶⠉⡘⢫⠈⠈⢿⣿⣿⣿⣿⣧⣤⡄ ⣿⣿⣿⣿⣿⣿⣯⣩⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣽⣿⣿⣶⡿⠋⠸⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢐⡀⠉⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣾⣷⡶⠚⣿⣿⣿⣶⣝⠩⠉⠍⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣽⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠉⡑⠉⢉⣢⠀⢂⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣉⠐⡊⠀⠹⡙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⡘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣦⡀⠹⠃⠀⢳⣿⣿⣕⢍⠂⠀⠉⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⢈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍ ⣿⣿⠀⠀⠛⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣐⡀⠀⠈⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⡘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠐⠀⠨⣼⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⠸⢻⣿⣿⣷⠕⠐⠄⠁⠀⠀⠬ ⣿⣿⣿⣆⡄⣀⡄⠈⣹⣧⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡈⠂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⢷⣿⣿⣷⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡦⠀⣰⣿⠃⠻⠦⠞⡿⠞⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⡊⠨⢿⣿⣿⣿⣿⣷⣄⡄ ⣿⣿⣿⣿⣿⣿⣯⣩⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣽⣿⣿⣶⡿⠋⠸⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢈⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣤⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⠩⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢿⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢄⣹⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡉⡁⠉⠉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣢⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠸⣿⣿⣿⣿⢟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠛⠢⠛⢛⣉⠐⡏⠈⠑⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⡿⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣁⠅⡂⠀⠈⣧⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⣀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉ ⣿⣿⠐⠚⠛⣿⢧⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢻⣭⣔⡀⠀⢨⣉⣧⣓⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠈⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠠⠀⡤⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⠅⠀⠐⠀⣾⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡷⠗⠄⠁⠁⠀⠬ ⣿⣿⣿⣆⣀⣀⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢿⣟⠋⡘⠂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⣿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⠻⡻⠮⠾⠿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢰⣶⠉⡙⢫⠈⠈⢿⣿⣿⣿⣿⣿⣤⡄ ⣿⣿⣿⣿⣿⣿⣯⡀⢿⣷⣂⠀⢵⣮⣃⣭⣿⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠳⠈⣴⣞⡃⠀⠴⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠂⢋⢈⢇⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣷⣿⣎⠻⢷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⠚⣿⣿⣿⣶⣝⠫⠭⢍⠉⡉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⡛⠿⢿⣿⡿⢿⡯⣿⡿⣿⣹⣯⠄⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡿⢹⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣯⣿⡍⡑⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⠀⠁⠀⢀⠐⠃⠀⠙⡄⠀⠅⠈⠁⠜⢈⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢿⣿⣿⠟⠛⠿⣟⡈⠻⣻⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢂⡀⠀⠀⠸⣾⠊⢳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡮⠉⣀⣀⠐⠙⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠈⠈⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⠀⠀⠀⢂⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⡠⠃⠉⡒⣿⣦⢏⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡄⠀⠀⠈⠡⠔⣀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣿⣶⣿⣿⡟⡘⡺⠛⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣛⠈⢀⠀⠀⠀⢀⣠⣶⢿⡙⣼⣕⡋⠰⡀⠀⠀⠈⠡⠸⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡂⠀⠀⠀⠐⠁⠬⠀⠀⠘⢏⡻⠉⠁ ⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⠿⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⡀⡋⠀⠀⠀⡐⢡⣍⡀⠀⠀⠉⡩⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠼⢃⣠⣿⣿⣿⢦⣼⣿⣧⣽⣿⣿⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠄⠀⢐⡄⠹⣿⣿⣿⣷⣦⣆⣠⡤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣾⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⠀⢀⣠⢮⢳⣿⣿⣿⣿⣿⣿⣟⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡨⠌⠉⢐⡨⠤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡈ ⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⡿⠿⠿⢿⣟⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢻⣿⣿⡇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⣿⣿⣿⣟⡾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠝⡐⢸⣿⡟⢠⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣿⣿⣿⢞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠛⠠⠛⢻⣉⠐⡏⠈⠙⡙⣿⣿⣿⣿⢏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿ ⣿⣿⠊⠙⣿⣿⡿⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣑⢍⡂⠀⢀⣇⡿⣿⣿⡟⢸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠃⣀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠍ ⣿⣿⠀⠘⠛⣿⢧⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⣻⣭⣔⡀⠀⠨⣉⣧⣓⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⡘⣿⣿⡀⡀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠠⠀⡤⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⢼⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⡷⠗⠄⠁⠀⠀⢬ ⣿⣿⣿⣆⣀⣀⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡄⢠⢾⣟⠋⡈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⢻⣿⡇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⠸⡻⠮⠟⠿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠈⢿⣿⣿⣿⣿⣿⣤⡄ ⣿⣿⣿⣿⣿⣿⣯⡀⢿⣧⣂⠀⢵⣮⣃⣭⣿⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠳⠈⣴⣞⡃⠀⠴⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⣇⢶⠀⠐⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣷⣿⣎⠛⢷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⠚⣿⣿⣿⣶⣝⠩⠉⢉⠉⡍⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣝⣿⡟⠻⢿⣿⡿⢿⡿⣿⡿⣿⣹⣯⠄⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⣄⣽⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢹⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡍⡑⠉⢉⣦⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣿⣷⣾⣿⠿⣟⣻⣯⣭⣽⣿⣿⣿⣿⣯⣭⣭⣥⣛⠛⠠⠛⢛⣉⠐⡊⠈⠉⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠊⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢉⣁⢅⡂⠀⠈⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠀⣠⠆⢹⣿⣿⠉ ⣿⣿⠒⠈⠛⢿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣻⣭⣴⡀⠀⠨⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠐⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠀⢀⠀⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠈⣼⣿⣿⣻⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠑⠄⠁⠀⠀⠨ ⣿⣿⣿⣆⡀⣀⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣿⢸⣟⠋⣈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⢷⣷⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⡻⠦⠞⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⠈⠈⢿⣿⣿⣿⣿⣷⣤⡅ ⣿⣿⣿⣿⣿⣯⡌⣟⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠰⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢐⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣷⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢣⣿⡟⣤⣤⣴⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠩⠭⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣧⢸⣿⢽⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢣⣿⠉⡁⠉⢉⣢⠀⢃⣀⣻⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣉⠐⡊⠉⠹⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠜⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢳⣿⣿⣗⢅⡂⠀⠀⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠂⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠊⢹⣿⣿⠉ ⣿⣿⠀⠈⠛⢿⣿⣿⣿⣿⡟⣼⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣿⣭⣴⡀⠀⠩⡉⣥⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⡀⣸⣿⣃⢰⣿⣷⣼⠀⢀⠈⠀⡀⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⣬⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠗⠄⠀⠀⠀⢨ ⣿⣿⣿⣆⣀⣀⡄⠈⣻⣧⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡈⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⢻⣿⣴⣶⣶⣤⡄⠀⠀ ⣿⣿⣿⣟⢛⣿⣿⣿⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡦⠀⣴⣿⠃⠻⠦⠿⡿⠞⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠈⠨⢿⣿⣿⣿⣿⣷⣄⡄ ⣿⣿⣿⣿⣿⣿⣯⣩⣽⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣾⣯⣭⣿⣿⣶⣿⠋⠰⠈⣴⣞⡃⠀⠴⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢨⢆⢶⠀⢒⡠⠉⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠩⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠰⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣿⠻⠿⢿⣿⡿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣷⢼⣿⢾⣿⡷⠀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠉⡁⠉⢩⣦⠀⢋⣀⣻⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡓⠑⣿⡛⠢⠛⢛⡉⠐⡊⠉⠹⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣭⣽⣷⣶⣶⣶⣶⣶⣶⣶⣤⣭⣈⠀⠀⢉⣁⠅⠂⠀⠀⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢐⡀⠀⠀⠄⣠⠎⢹⣿⣿⠍ ⣿⣿⠂⠈⠛⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢻⣭⣔⡀⠀⠩⡉⣥⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣾⠐⢀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⣿⣿⡍⠙⢿⡏⠀⣾⣿⣽⣷⣦⣹⣿⣿⢅⠀⠐⠠⣾⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠖⠄⠀⠀⠀⠬ ⣿⣿⣿⣆⡀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⣏⣟⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣼⣶⣶⣤⡄⠀⠈ ⣿⣿⣿⣟⢿⣿⣿⢰⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⢮⠗⡿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⠫⡈⠈⢿⣿⣿⣿⣿⣷⣄⡄ ⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠈⣴⣞⡃⠀⠰⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢈⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣷⡜⠿⣿⣿⣿⣷⣽⣿⣿⣿⢿⣫⣾⢁⣶⣢⡀⢼⣾⡦⣭⣤⣴⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠋⠉⠍⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣙⣿⠟⠻⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠊⢻⣷⣿⣿⣿⣿⣷⢼⣿⢽⣿⡷⠄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡟⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠛⠂⠀⠁⠀⢀⠐⠃⠀⠛⣄⠈⠅⠈⠁⠄⢈⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠂⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣔⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡉⢀⠀⠀⠀⠸⣷⠊⠳⢦⣇⡠⢽⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠐⠙⠁⡀⠀⠀⠀⢠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣥⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⠠⠃⠋⡂⣯⣤⢋⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠈⠀⣴⠈⢁⡤⡀⠀⠀⠡⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣿⣿⣿⣶⣿⣿⡟⡚⡺⠚⠋⢉⠄⠀⠃⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢁⢙⣫⡿⠛⠉⢋⣑⡀⢈⠠⠂⠀⢀⣠⣶⢟⡙⣴⣝⡃⠀⡀⠀⠀⠀⠠⠘⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⡀⠀⠀⠀⠀⠁⠈⠀⠀⠘⢍⡛⠉⠁ ⣿⣾⣿⣿⣿⣿⣿⣷⡆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⠻⣿⣿⣘⣿⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠀⣐⡀⡈⠀⠀⠀⠀⢠⣁⡀⠀⠀⠉⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢃⣠⣿⣿⡿⢦⣬⣿⣥⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡝⠄⠀⢀⠄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣾⣿⣿⡿⣿⣿⣿⡿⠟⠻⠟⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣗⠀⢀⠠⢪⢳⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡠⠌⠉⢐⡈⠴⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠌⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⡇⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠀⠀⠀⢬⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⣿⣿⡿⣟⣾⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠹⠀⢸⣿⡟⢡⣿⣿⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠠⠛⢹⡉⠐⡋⠉⠹⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠈⣀⠉⠈⠀⠀⢉⣁⠅⠂⠀⠀⣆⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉ ⣿⣿⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠩⣉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣼⠐⠀⠨⠀⡀⠻⠷⡀ ⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠊⠙⠟⢿⣿⠄⠘⣿⣿⣿⠅⠀⠀⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠕⠑⠄⠀⠀⠀⠬ ⣿⣿⣿⣆⡀⡀⢀⣈⣛⣻⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢉⣀⣀⣀⠊⢻⡧⢤⢾⣟⠋⡘⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣴⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⡏⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣠⣶⣶⣮⡻⣿⣿⣿⣿⣦⠀⣉⡺⡻⢦⠗⠿⠖⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠈⠈⢿⣿⣿⣿⣿⣷⣄⡄ ⣿⣿⣿⣿⣇⣿⣿⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⡇⠀⠡⠈⣴⣞⡃⠀⠴⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢐⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⡜⢿⣷⣭⣛⣛⣛⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⣤⣤⣶⣿⣿⣷⣾⣷⣶⠞⣿⣿⣿⣶⣝⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⢿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⡧⠂⢹⣷⣿⣾⣯⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣷⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡍⡁⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠑⣿⡋⠠⠛⢙⡍⠐⡋⠉⠹⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠈⣀⠉⠈⠀⠀⢉⣁⠅⠂⠀⠀⣇⡾⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢐⡀⠀⠠⠄⣠⠊⢹⣿⣿⠉ ⣿⣿⠂⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣦⣶⣶⠀⠈⢻⣭⣔⡀⠀⠨⣉⣷⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⠀⠈⠀⡀⠻⠷⡀ ⣿⣿⡄⠀⠀⠨⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠊⠙⠟⢿⣿⡄⠘⣿⣿⣿⠅⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠐⠄⠀⠀⠀⠨ ⣿⣿⣿⣆⡄⡀⢀⣀⣛⣻⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⣀⣀⣀⠈⠻⡧⢤⢾⣟⠋⡘⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣾⣶⣶⣤⡄⠀⠈ ⣿⣿⣿⣟⡇⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠀⣠⣶⣶⣮⡻⣿⣿⣿⣿⣦⠀⣉⡺⠻⠮⠟⠿⠞⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠈⠈⢿⣿⣿⣿⣿⣷⣄⡄ ⣿⣿⣿⣿⣇⣿⣿⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⡇⠀⠡⠈⣴⣞⡃⠀⠤⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢒⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⡜⢿⣷⣭⣛⣛⣛⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⣤⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⢿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⡷⠂⢹⣷⣿⣾⣯⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡍⡁⠉⢩⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠛⠠⠛⢻⣩⠐⡏⠀⠩⡙⣿⣿⣿⣿⢏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⡿⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢉⣁⢍⡂⠀⠈⣖⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣆⠀⡀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⣀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉ ⣿⣿⠀⠈⠛⣿⢣⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢻⣭⣴⡀⠀⠨⣉⣧⣑⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⡀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡤⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢪⣄⠀⠀⢿⢿⡇⠀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠓⠄⠁⠀⠐⠬ ⣿⣿⣿⣆⡒⣄⠼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢾⣟⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣀⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⣻⣿⣼⣶⣶⣤⡄⠀⠀ ⣿⣿⣿⣟⣻⣿⣇⠛⢁⣤⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡺⡻⠮⠟⡿⠞⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢰⣶⠉⡙⢫⠈⠈⢿⣿⣿⣿⣿⣿⣤⡅ ⣿⣿⣿⣿⣿⣿⣯⡀⢿⣧⣂⠀⣵⣮⣉⣭⣭⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠳⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⢆⢶⠀⢲⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣷⣿⣎⠛⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣤⣤⣴⣶⣿⣿⣿⣾⣷⣶⠞⣿⣿⣿⣶⣝⠋⠩⠉⠉⠍⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⡟⠿⢿⣿⡿⢿⡿⣿⣿⣿⣹⣯⠄⢿⣿⣿⣿⣿⣿⣷⢸⣿⢾⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡍⡁⠉⢉⣦⠀⢋⣠⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⢟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠋⠠⠛⢻⣭⠐⠋⠀⢡⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠠⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡂⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⡟⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢉⣁⢍⠂⠀⠈⣆⡿⣿⣿⡟⣸⡇⠠⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⣀⡀⠀⠠⡄⣠⠎⢹⣿⣿⠉ ⣿⣿⠂⠈⠛⣿⢧⣿⣿⢷⡀⠈⠁⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢻⣭⣴⡀⠀⠨⣉⣧⣛⡇⣿⠃⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠐⡘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⢀⠈⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠁⣈⣭⣭⣭⣭⣝⢪⣔⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⠻⣿⣿⣷⠵⠕⠄⠁⠀⠀⢬ ⣿⣿⣿⣆⡀⣄⡼⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢿⣟⠋⡘⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠂⠀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢰⣀⠉⢿⣿⣼⣶⣾⣤⡄⠀⠈ ⣿⣿⣿⣟⣿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡺⡻⠮⠟⡿⠞⠀⠀⣀⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⡌⠈⢿⣿⣿⣿⣿⣿⣤⡄ ⣿⣿⣿⣿⣿⣿⣯⡀⢿⣧⣂⠀⣵⣮⣋⣭⣽⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠳⠈⣵⣞⡃⠀⠤⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣅⠀⢋⢈⣆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⡎⠻⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣤⣤⣴⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠍⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠿⢿⣿⡿⢿⡿⣿⣿⣿⣹⣯⠀⢿⣿⣿⣿⣿⣿⣷⢸⣿⢾⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡿⢹⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠍⡑⠉⢉⣦⠄⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠂⠀⠀⠀⢀⠐⠃⠀⠙⣆⠈⠅⠈⠉⠴⢈⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⡀⠀⠀⠸⣶⠊⢳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⡀⠀⠀⠂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⡠⠂⠉⠒⣿⣦⢞⢣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠀⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣵⣿⣿⣿⣶⣿⣿⡟⡘⡳⠚⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⡃⠀⣀⠀⠀⠀⠠⠘⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⢀⠀⠁⠨⠀⠀⠘⢏⡛⠉⠁ ⣿⣽⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⣿⣻⡆⢉⣿⣿⢻⣿⣿⣘⣿⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⠀⡂⠀⠀⠀⠐⢀⣁⡀⠀⠀⠉⡈⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠘⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡚⠄⠀⢀⡄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⡯⣾⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣗⡀⢀⢠⢪⢳⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢻⡨⠬⠉⢐⡈⢤⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡀ ⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠆⣰⣿⣅⣡⣴⣿⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆⠠⠀⠀⢏⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⢿⣿⣿⢻⣾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣏⠝⠀⢸⣿⡟⢡⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣷⣿⣿⣾⣿⣾⣿⠿⣟⣻⣯⣭⣽⣿⣿⣿⣿⣿⣭⣥⣥⣛⠛⠠⠛⢛⡩⠐⡋⠈⠩⠙⣿⣿⣿⣿⢏⣾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢉⣁⢅⠂⠀⠈⣆⡾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠉ ⣿⣿⠂⠈⠛⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠨⢻⣭⣴⡀⠀⠨⣉⣷⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣼⠐⠀⠈⠀⡤⠻⠿⡀ ⣿⣿⡄⠀⠀⠀⣾⣿⣿⣻⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⣿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠗⠔⠄⠁⠀⠐⢬ ⣿⣿⣿⣆⣀⡀⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣷⢸⣟⠋⡨⢂⡀⠀⠙⠉⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣼⣶⣾⣤⡄⠀⠈ ⣿⣿⣿⣟⢿⣷⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⡹⠦⠟⡿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠈⠈⢿⣿⣿⣿⣿⣷⣄⡄ ⣿⣿⣿⣿⣿⣿⡌⣞⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠲⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢰⡠⠉⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣷⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢣⣿⡟⣤⣤⣴⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡉⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠂⠀⠀⠀⢀⠐⠃⠀⠙⣀⠈⠅⠈⠃⠔⢈⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣖⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⢸⣿⣿⣿⠌⠀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⣅⣧⣡⢀⠈⠀⠀⠀⢂⠐⡈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⡠⠂⠋⠒⣯⣦⢞⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣠⣦⣼⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠋⠀⣴⠈⢁⡤⠀⠀⠀⠠⠔⢀⠅⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⣷⣿⣿⣿⣶⣿⣿⡞⡘⡺⠚⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠿⢃⢙⣫⣿⠛⠉⢛⣛⠀⢀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣕⣃⠀⣀⠀⠀⠀⠠⠘⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠁⠌⠀⠀⠘⢏⡛⠉⠁ ⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣿⣿⢻⣿⣿⣘⣿⣶⣦⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⣐⢀⡂⠀⠀⠀⠐⢠⣅⡀⠀⠀⠉⡈⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠜⢃⣠⣿⣿⡿⢦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⠄⠀⢀⠄⠹⣿⣿⣿⣷⣦⣄⣠⡤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢤⣾⣿⣿⠯⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣍⠛⠿⢿⣿⣿⣯⣖⣀⢀⣠⢪⢳⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢻⡈⠌⠉⢐⡈⠤⣢⣶⣾⣿⣿⡿⣻⡽⠞⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠋⢿⣿⣿⡀ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⡇⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢮⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣲⣿⣿⣿ ⣿⣿⣷⠘⣿⣿⣿⣏⣾⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣏⠝⠀⢸⣿⡟⢡⣿⣧⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿⢿⣿⣿⣛⣛⣻⠿⠋⠃⠑⣿⡋⠠⠛⢛⡩⠔⡋⠀⢹⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⡿⡿⣿⡟⠒⢀⣭⡈⠀⠀⢉⣁⠅⠂⠀⠈⣇⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠄⢈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠀⣠⠎⢹⣿⣿⠍ ⣿⣿⠀⠀⠛⣿⣿⣿⡿⣫⣶⣿⣿⡿⣻⣿⣿⣟⣷⣶⡀⠙⠃⠐⢸⣿⣿⣶⠀⠈⢻⣭⣴⡀⠀⠨⣉⣧⣑⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠂⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣼⠐⢀⠀⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⣬⡟⣼⣿⣿⣿⣏⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠇⠀⠀⠠⣾⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⣿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠵⠖⠄⠁⠀⠀⠬ ⣿⣿⣿⣆⡀⣀⡄⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⢾⣟⠋⡈⢂⠀⠀⠙⠉⣇⢻⣷⣄⣐⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⢿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⣻⣿⣼⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⢟⣿⣇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⡀⠀⠀⡘⣯⣝⣋⠀⠚⡻⢦⠟⡿⠖⠀⠀⣀⣾⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠀⠈⢿⣿⣿⣿⣿⣷⣄⡄ ⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⣟⣷⣿⣰⣗⠀⠨⣷⣌⣛⠏⠀⠣⠈⣴⣞⡃⠀⠴⠀⢻⣿⣷⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⣇⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣄⣼⣿⣿⡏⣴⣤⣤⣶⣿⣿⣷⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠩⠉⠉⠍⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠉⡁⠉⢉⣢⠀⢃⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠃⡲⣀⡛⣉⠔⡋⠈⠩⠙⣿⣿⣿⣿⢏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⢀⢹⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣦⡀⠹⠃⠀⢳⣿⣿⣕⢅⠂⠀⠈⣆⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠂⠈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉ ⣿⣿⠂⠀⠛⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣴⡀⠀⠨⣉⣧⣙⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣾⠐⠀⠀⠀⡄⠻⠿⡀ ⣿⣿⡄⠀⠀⠠⣬⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢻⣿⣿⣷⠷⠖⠄⠁⠀⠀⢬ ⣿⣿⣿⣆⡀⣀⡄⢈⣹⣧⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡈⢂⡀⠀⠘⠉⣇⢻⣷⣄⣂⠠⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⢉⢸⣿⢸⣀⠉⣻⣿⣴⣶⣾⣤⡄⠀⠈ ⣿⣿⣿⣟⢛⣿⣿⣿⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣳⡇⣸⡆⠀⣰⣿⠁⡹⠦⠟⡿⠖⠀⠀⣠⣼⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡘⢫⠀⠈⢿⣿⣿⣿⣿⣷⣄⡄ ⣿⣿⣿⣿⣿⣿⣯⣯⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣾⣿⣽⣿⣿⣶⡿⠋⠰⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢲⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⣤⣶⣿⣿⣷⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠍⠉⠉⠉⠉⠉⠉⠩⢄⣀⣤⣶⣿⠇⠐⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢿⣟⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢼⣿⡷⢄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⠍⡁⠉⢉⣢⠀⢋⣀⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠂⠀⠀⠀⢐⠐⠃⠀⠙⣄⠈⠁⠈⠃⠔⢈⢝⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠃⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢿⣿⣿⣿⣿⣿⣿⣿⡧⠉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠤⡀⠉⠻⠿⣿⣿⣿⣿⣿⠟⠋⠁⡀⠀⡅⣕⣡⢀⠈⡀⠀⠀⢀⠐⠈⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⠀⠂⠉⠂⢷⢦⣧⢧⢸⣦⣀⣠⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣶⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠈⠀⣴⠈⢁⡄⠀⠀⠀⠠⠐⢀⣁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡳⣵⣿⣿⣿⣶⣿⣿⣟⡈⢳⠚⠉⢉⢀⠀⠀⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠟⢀⢙⣫⣿⠛⠉⣋⣛⠈⢀⠠⠀⠈⢀⣠⣶⢿⡙⣼⣔⡃⠀⡀⠀⠀⠀⡠⠰⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⡀⠀⠀⢀⠀⢁⢌⠀⠀⠈⢉⡛⠉⠀ ⣿⣼⣿⣿⣿⣿⣿⣷⡄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⣿⠻⣿⣿⣘⣿⣷⣴⣖⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⢀⠉⠀⠀⠀⠁⢠⣍⡀⡀⠀⠉⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣙⠸⢃⣠⣿⣿⣿⢤⣼⣿⣤⣽⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡓⡀⠀⢐⠆⡸⣿⣿⣿⣷⣦⣆⣠⠄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣼⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣇⢀⠀⢠⢦⢰⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣋⣿⣿⢫⡈⠌⠉⠀⡀⢰⣠⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⢈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠙⢿⣿⣧⡈ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠂⣸⣿⣍⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢉⢻⣿⣿⣿⣿⣿⣿⣿⢿⢋⣄⣲⣿⣿⣿ ⣿⣿⣷⠘⢿⣿⡿⣛⣿⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠻⡀⢸⣿⡟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠀⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠠⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡃⠑⣿⡏⠠⠛⢛⣭⠐⠏⠀⠀⡙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡂⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢟⣛⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣭⣈⠀⠀⢉⣁⢅⡂⠀⠀⣆⠾⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠄⣠⠏⢹⣿⣿⠉ ⣿⣿⠀⠈⠛⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣭⣴⣀⠀⢨⣉⣥⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣷⣮⠂⢀⠠⠀⡄⠻⠿⠀ ⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⡿⣿⡍⠙⢿⡏⠀⣾⣿⣽⣷⣦⣹⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠵⠄⠁⠀⠀⠌ ⣿⣿⣿⣆⣐⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⡐⠂⠀⠀⠝⠩⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢰⡀⠈⣹⣿⣼⣶⣾⣤⡄⠀⡈ ⣿⣿⣿⣟⣿⣿⣿⢐⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⡻⠦⠾⡿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠌⠈⢿⣿⣿⣿⣿⣿⣤⡅ ⣿⣿⣿⣿⣿⣿⣭⡀⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠘⣴⣞⡃⠀⠀⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢀⢆⢶⠀⠱⡀⠙⣿⣿⣿⣿⣷⣬ ⣿⣿⣿⣿⣿⣿⣿⣷⡜⠻⣿⣿⣿⣷⣽⣿⣿⣿⢿⣫⣾⢡⣶⣢⡀⢼⣶⡦⣭⣤⣤⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣙⣿⠟⠟⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠚⢻⣷⣿⣿⣿⣿⣧⢸⣿⢽⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡿⢹⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢡⣿⡉⡁⠉⢉⣢⠂⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠟⠂⠀⠀⠀⢀⠐⠁⠀⠉⡀⠈⠅⠈⠁⠔⢈⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠗⠛⠿⢟⠨⠛⣻⠩⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠁⠀⠠⡀⠀⠠⠀⠀⠀⠀⢀⠁⠀⠀⠀⠠⢖⡓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⡏⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⡦⡉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠀⢀⠀⠀⠈⠘⠀⠘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠄⠀⠉⠻⠿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⡅⣄⡡⢀⠈⠀⠀⠀⢀⠐⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡁⠀⠀⠀⠂⠉⠂⣷⣦⣁⢣⣰⣦⣀⣠⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣶⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠌⠈⠀⣴⠀⢁⡄⠀⠀⠀⠠⠐⢀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢓⣿⣾⣿⣿⣶⣿⣿⣝⡀⠃⠚⠉⠉⢀⠀⠀⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠛⢀⢙⣫⣿⠛⠉⢋⣓⠀⠀⠠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡁⠀⡀⠀⠀⠀⠠⠐⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠁⢌⠀⠀⠈⠌⡙⠉⠀ ⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣾⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⡟⠻⣿⣿⣐⣿⣶⣴⣔⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣐⢀⠁⠀⠀⠀⠀⢀⣁⡀⠀⠀⠁⡈⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⢃⣠⣿⣿⡿⢤⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡗⠀⠀⢀⠄⠸⣿⣿⣿⣷⣦⣄⣀⠄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠯⣾⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣧⣗⠀⠀⢠⢠⢲⣾⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢋⣿⣿⢣⡀⠈⠉⠀⡀⠠⣂⣶⣾⣿⣿⡿⣻⡵⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣧⣾⣾⣿⣿⣿⣿⣿⣿⠋⢿⣿⣧⡈ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⠈⢱⣿⣿⠂⣰⣿⢁⣠⣴⣿⣿⣿⣿⠿⣣⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢩⢻⣿⣿⣿⣿⣿⢿⣿⣿⠋⣄⣲⣿⣿⣿ ⣿⣿⣷⠘⢿⣿⡿⢛⣷⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠛⠀⢸⣿⠟⢠⣿⢧⣼⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠁⠀⠀⠀⠀⠉⠩⣴⣿⣿⣿⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡃⠑⣿⡏⠠⠛⢛⣯⠐⠏⠀⠠⡙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⣠⠈⠈⠀⠀⢉⣁⢅⡂⠀⠈⢆⠾⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠂⢀⡀⠀⠠⠀⣠⠌⢹⣿⣿⠉ ⣿⣿⠂⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢤⣿⣦⣶⣶⠀⠘⢻⣭⣤⡀⠀⢬⣉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣮⠂⢀⠨⠀⡤⠿⠿⡀ ⣿⣿⡄⠀⠀⠩⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠚⠙⠟⢿⣿⠄⠈⣿⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠷⠷⠄⠀⠁⠀⠬ ⣿⣿⣿⣆⡐⡀⢀⣈⣛⣻⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢉⣀⣀⣀⠊⠻⡧⢤⢿⣟⠋⡌⠂⠀⠀⠝⠩⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢰⣀⠈⢻⣿⣾⣶⣾⣤⡤⠀⠈ ⣿⣿⣿⣟⠏⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠄⠀⠀⣠⣶⣶⣮⡻⣿⣿⣿⣿⣦⠘⣉⠚⡻⠦⠟⡿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡙⢫⠊⠈⢿⣿⣿⣿⣿⣷⣤⡅ ⣿⣿⣿⣿⣇⣿⣿⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣇⠀⠳⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢀⢆⢖⠀⢑⡀⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⡜⢿⣷⣭⣛⣛⣛⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣿⣶⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⡷⠂⢹⣷⣿⣾⣯⣿⣿⣿⣿⣿⠿⢿⣯⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣿⣿⣿⣿⣿⡗⣿⣾⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣧⣿⡉⡁⠉⢉⣠⠀⢃⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠂⠀⠀⠀⢐⠐⠁⠀⠙⡀⠘⠅⠈⠂⠔⢈⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⢟⠈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢈⠁⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⣲⠛⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⢹⣍⢀⠀⠀⠀⠸⣿⠊⠷⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡧⣉⣀⣀⠀⠙⢁⡀⠀⠀⠀⠠⠀⢀⠀⠀⠈⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠤⣀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠋⠁⡀⠀⡇⣷⣥⠂⠈⡀⠀⠀⢀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⢀⡠⠃⠉⠒⣿⣦⣧⢧⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠀⠀⣴⠈⢁⡄⡀⠀⠀⠡⠐⢀⡁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿⣿⣿⣶⣿⣿⣿⡜⠻⠛⠉⢉⠀⠀⠂⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡀⠀⠀⢸⣿⣿⠟⢂⢙⣿⣿⠛⠉⢛⣛⡘⠈⢠⢀⠀⢀⣠⣶⢟⡙⣼⣝⡋⠰⡀⠀⠀⠈⠠⠰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠉⢈⠀⠀⠈⢍⡛⠉⠁ ⣿⣼⣿⣿⣿⣿⣿⣿⡆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⠻⣿⣿⣘⣿⣶⣴⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⣐⢀⡉⠀⠀⠀⡐⢠⣍⡀⣀⠈⠁⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣉⠸⢓⣤⣿⣿⣿⣮⣬⣿⣧⣽⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⢀⡦⡹⣿⣿⣿⣿⣦⣆⣀⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢬⣾⣿⣿⠿⣽⣿⣿⠿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⡛⠿⢿⣿⣿⣯⣗⢀⠀⣠⢢⢻⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣿⣿⢫⡨⠬⠉⠀⡨⢴⣂⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡅⠠⢈⠙⢿⣻⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡨ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⡿⠿⠿⢿⣻⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣍⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⢿⣿⣿⣛⡾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠻⠀⢸⣿⡟⢠⣿⣯⣴⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠀⠀⠄⠀⠉⠹⣴⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠃⠀⠀⠀⢐⠐⠃⠀⠙⡀⠈⠅⠈⠃⠴⢈⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⡨⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢉⠁⠀⠠⢀⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠠⠠⣴⡛⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢀⡀⠀⠀⠸⣿⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⡦⣉⣀⣀⠈⠙⢁⣀⠀⠀⠀⡠⠀⢀⠀⠀⠈⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⠿⣿⣿⣿⣿⣿⠟⠋⠁⡀⠀⡅⣦⣥⠂⠈⠀⠀⠀⢀⠐⠈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⠀⠃⠉⠒⣿⣦⣧⢧⢸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣟⣉⣠⣶⣰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠀⠀⣴⠀⢁⡄⠀⠀⠀⠡⠐⢀⠁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣿⣿⣿⣿⣶⣿⣿⣟⡈⢻⠚⠉⢉⠀⠀⠃⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠁⠀⢸⣿⣿⠟⢀⢙⣫⣿⠛⠉⣋⣛⡀⢈⢠⢀⠀⢀⣠⣶⢟⡙⣴⣝⡓⠠⡀⠀⠀⠈⠠⠰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⠀⠀⠉⢈⠀⠀⠈⠍⡻⠉⠀ ⣿⣼⣿⣿⣿⣿⣿⣷⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⠆⢉⣾⣿⠹⣿⣿⣘⣿⣶⣴⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⢀⠋⠀⠀⠀⡀⢠⣍⡀⠀⠀⠉⡸⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠸⣓⣤⣿⣿⣿⣦⣬⣿⣤⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡗⠀⠀⢠⠆⡸⣿⣿⣿⣷⣦⣄⣀⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⢤⣾⣿⣿⠿⣿⣿⣿⠿⠟⠛⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣖⢀⠀⣠⢢⢻⣿⣿⣿⣿⣿⣿⣏⣩⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣿⣿⢣⡨⠈⠉⠀⡈⢤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⠿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣧⡈ ⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⠆⣰⣿⣉⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⠀⠀⢩⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣖⣿⣿⣿ ⣿⣿⣷⠘⢿⣿⣿⣏⣾⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣏⠛⠀⢸⣿⠟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢊⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡹⠁⠀⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠠⣿⣿⣿⣿⣾⣿⣾⣿⠿⣛⣻⣯⣭⣭⣿⣿⣿⣿⣯⣭⣭⣥⣛⠋⠠⠛⢛⣯⠔⠏⠀⠨⡙⢿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⣑⢍⡂⠀⠈⢆⠾⡿⣿⡟⣸⠇⠀⠀⠝⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⠀⢸⣿⡇⠃⢀⠀⠀⠠⠄⣠⠞⢹⣿⣿⠉ ⣿⣿⠀⠈⠛⢿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢻⣭⣴⡀⠀⠬⣉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠋⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣷⣮⠂⠀⠠⠀⡤⠻⠿⡀ ⣿⣿⡄⠀⠀⠈⣼⣿⣿⣿⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⠃⠀⠀⠢⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⠿⣿⣿⣿⠵⠷⠄⠁⠀⠈⠬ ⣿⣿⣿⣆⡀⡄⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⡻⣿⣿⣿⣿⣷⢸⣟⠋⡔⠂⡀⠀⠙⠩⣇⢻⣷⣄⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢸⣀⠈⢻⣿⣾⣶⣶⣤⡄⠀⠈ ⣿⣿⣿⣟⢷⣷⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⡻⠦⠿⡿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠊⠈⢻⣿⣿⣿⣿⣿⣤⡄ ⣿⣿⣿⣿⣿⣿⡌⣟⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠠⠘⣴⣞⡃⠀⠠⠀⢿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢀⢆⢶⠀⢒⡀⠛⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣷⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢣⣿⡟⣤⣤⣤⣶⣿⣿⣿⣶⣷⡶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠍⠉⠉⠉⠉⢀⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⣿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣷⢸⣿⢽⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠁⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢧⣿⡉⡑⠉⢉⣠⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⠿⣛⣻⣯⣭⣽⣿⣿⣿⣿⣯⣭⣥⣥⣛⠋⠠⠛⢻⣭⠐⠏⠀⠸⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⢀⢀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⡿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⣑⢅⠂⠀⠀⢇⡿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⠀⠀⢀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡇⠆⢀⡀⠀⠠⠄⣠⠞⢹⣿⣿⠍ ⣿⣿⠂⠈⠛⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢻⣭⣔⡀⠀⢨⡉⣧⣓⡆⣿⠀⠀⠀⠀⠐⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠸⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣮⠀⢀⠈⠀⡤⠻⠿⡀ ⣿⣿⡄⠀⠀⠈⣼⣿⢿⣿⣟⣻⣿⣿⡛⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠷⠕⠄⠁⠀⠈⢬ ⣿⣿⣿⣆⡀⡄⣿⢿⣿⣿⣿⣿⣯⠻⠆⠀⠃⠀⠠⢿⣷⣶⣶⣯⣻⣿⣿⣿⣿⣷⢘⣟⠋⡀⢂⡀⠀⠙⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣶⣶⣾⣤⡄⠀⠈ ⣿⣿⣿⣟⢿⣧⢻⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⡻⠮⠷⠿⠖⠀⠀⣠⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠈⠘⢿⣿⣿⣿⣿⣿⣤⡅ ⣿⣿⣿⣿⣿⣿⡌⣞⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠲⠘⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⢙⠻⠿⢟⣃⠀⢋⢀⣆⢶⠀⢰⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣌⢮⣛⣛⣛⣫⠞⣡⣀⠀⣀⢰⣈⣿⣿⣿⣿⡿⢃⣿⡟⣤⣤⣤⣶⣿⣿⣷⣶⣷⡶⠚⣿⣿⣿⣶⣝⠉⠍⠉⠉⠉⠉⠉⠩⠉⠉⣀⣀⣤⣶⣿⠇⠰⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⠿⢿⣷⡟⢸⡿⣿⡿⣿⢿⣿⠉⢿⣿⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⣀⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢥⣿⡍⡙⠉⢉⣢⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿⢿⣿⣿⣛⣛⣛⠿⠋⠃⠑⣿⡛⠠⠛⢛⣭⠰⠎⠀⠨⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⢿⣫⣵⣾⣿⣿⣿⣿⡿⡿⣿⡟⠒⢀⣭⡈⠀⠀⢉⣁⠅⠂⠀⠀⣇⠿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢈⢿⣿⣇⠀⢀⢸⣿⡇⠢⢀⡀⠀⠠⠄⣠⠎⢹⣿⣿⠉ ⣿⣿⠀⠈⠛⢿⣿⣿⡿⣫⣶⣿⣿⣿⣻⣿⣿⣟⣷⣦⡀⠙⠃⠀⢸⣿⣿⣶⠀⠘⢻⣭⣔⡀⠀⢨⡉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠸⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣮⠂⢀⠈⠀⡤⠻⠿⡀ ⣿⣿⡄⠀⠀⠨⣬⡟⣼⣿⣿⣿⣟⣾⣿⣿⣿⣿⣷⡄⠁⠀⠀⠀⠸⣿⣿⣿⣇⠈⣿⣿⣿⠅⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠕⠄⠁⠁⠈⠨ ⣿⣿⣿⣆⣀⣀⡔⣸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⠠⢞⣟⠋⡄⠂⡀⠀⠙⢉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣾⣶⣾⣤⡄⠀⠈ ⣿⣿⣿⣟⢻⣿⡇⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⢀⡄⠀⠀⠀⡘⣯⣙⣋⢀⠸⠻⠦⠿⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠈⠨⢿⣿⣿⣿⣿⣿⣤⡄ ⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣻⣿⠿⣟⣧⣿⣰⣗⠄⠨⣷⣌⣛⠏⠀⠳⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠀⢋⢠⢆⢶⠀⢰⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣄⣼⣿⣿⡏⣤⣤⣤⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⢀⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠛⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⢿⣿⣿⣿⣿⣿⣷⢸⣿⢿⣿⡷⣄⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣷⣿⡗⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢧⣿⡍⡙⠉⢉⣦⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠂⠀⠀⠀⢀⠐⠃⠀⠙⡄⠀⠅⠈⠁⠴⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠗⠛⠿⣟⠈⠛⣻⠹⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠠⣀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⣖⠓⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢀⡀⠀⠀⠸⣾⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⣯⠉⣀⣀⠀⠙⠁⡀⠀⠀⠀⠠⠂⢠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠄⡀⠉⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⡅⣧⣡⢀⠈⡁⠀⠀⠀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠂⠋⠂⣿⣤⣮⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⣉⣰⣶⣤⣿⣿⣿⠟⠉⠀⠀⠀⠀⠌⠂⠀⣴⠀⢁⡤⠀⠀⠀⠡⠐⢀⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣽⣿⣿⣿⣶⣿⣿⡟⡘⠻⠛⠉⢉⢄⠀⠂⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢀⢙⣻⣿⠛⠉⢋⣓⠐⠀⢠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡃⠠⡀⠀⠀⠈⠠⠸⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⠀⠀⠀⢈⠀⠀⠘⢋⡻⠉⠀ ⣿⣼⣿⣿⣿⣿⣿⣿⣄⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣴⣴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⣐⢀⠁⠀⠀⠀⠀⣠⣉⡂⠀⠀⠉⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣙⠸⢃⣠⣿⣿⡿⣦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⠀⠀⠐⠆⡹⣿⣿⣿⣷⣦⣄⣀⡄⠀⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⡿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⢀⢀⢠⢢⢠⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣽⣿⢫⡠⠌⠉⠑⡈⢤⣢⣾⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⣅⠀⠈⠙⢿⣿⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡂ ⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠃⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢱⣿⣿⡆⣰⣿⣅⣥⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⢀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⢿⣿⣿⢟⣷⡋⣼⣿⣿⣿⡿⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⠙⠀⢸⣿⡟⢠⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⡀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣭⠐⠏⠀⠨⡙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⡀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢱⣿⣿⡕⠅⠂⠀⠀⣇⡿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡆⠂⢀⡀⠀⠠⠄⣠⠞⢹⣿⣿⠉ ⣿⣿⠀⠀⠛⢿⣿⣿⣿⣿⡏⣾⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣴⡀⠀⠨⡉⣧⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⠀⠀⠀⡀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣮⠀⢀⠈⠀⡤⠿⠿⡀ ⣿⣿⡄⠀⠀⠨⣬⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠗⠕⠄⠀⠀⠈⢬ ⣿⣿⣿⣆⡀⣀⡔⠈⣻⣷⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡀⢂⡀⠀⠝⢉⣇⢻⣷⣄⣂⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠈⢻⣿⣾⣶⣾⣤⡄⠀⠈ ⣿⣿⣿⣟⢿⣿⣿⣶⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡆⠀⣰⣿⠃⠹⠦⠷⠿⠶⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡉⢻⠈⠈⢿⣿⣿⣿⣿⣿⣤⡅ ⣿⣿⣿⣿⣿⣿⣯⣭⣽⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣯⣽⣿⣿⣶⣿⠋⠰⠈⣴⣞⡃⠀⠠⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣃⠂⢋⢨⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣤⣤⣴⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠩⠉⠉⠉⠉⠉⠩⠉⠉⣀⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠛⠿⢿⣿⡿⣿⣿⣿⣿⣿⢻⣟⠉⢿⣿⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⣀⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠈⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⣥⣿⡉⡙⠉⢉⣢⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⣶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠂⠀⠀⠀⢐⠐⠃⠀⠙⡄⠨⠀⠈⠁⠴⣈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⠀⣀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⣶⠓⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡍⢀⠀⠀⠀⠸⣶⠊⠳⢦⣇⡤⢽⣿⣿⣿⣿⣿⣿⣿⣧⠉⣀⣀⠐⠛⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠀⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠌⡀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠛⠁⡀⠀⡅⣧⣡⢀⠈⡁⠀⠀⠀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠂⠋⠂⣿⣤⣮⢡⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣉⣰⣶⣤⣿⣿⣿⠟⠉⠂⠀⠀⠀⠌⠂⠀⣴⠀⢁⡤⠀⠀⠀⠡⠐⢀⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⣽⣿⣿⣿⣶⣿⣿⡟⡘⠻⠛⠉⢉⢄⠀⠂⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⡈⠀⠀⢸⣿⣿⠿⢀⢙⣻⣿⠛⠉⢛⣓⠐⢀⢠⠀⠀⢀⣠⣶⢟⡙⣤⣄⡃⠠⡀⠀⠀⠈⠠⠸⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⡀⠀⠀⠀⠀⠀⢈⠀⠀⠘⢋⡻⠉⠀ ⣿⣼⣿⣿⣿⣿⣿⣿⣆⣠⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣧⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣴⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⣔⡀⠁⠀⠀⠀⠀⣠⣉⡂⠀⠀⠉⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣙⠼⠃⣠⣿⣿⡿⣦⣬⣿⣤⣽⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠀⠀⢐⠆⡸⣿⣿⣿⣷⣦⣆⣀⡄⠀⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⠿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⢀⠀⢠⢢⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢣⡠⠌⠉⠐⡈⢴⣢⣾⣾⣿⣿⡿⣻⡽⠞⠉⠛⠻⢿⣿⣿⣿⣿⣷⣅⠀⠈⠙⢿⣿⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⡂ ⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠏⣀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣥⠈⢱⣿⣿⠆⣰⣿⣍⣤⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⢀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣄⣶⣿⣿⣿ ⣿⣿⣷⠘⢿⣿⣿⣟⣷⡋⣼⣿⣿⣿⣿⣫⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣍⡙⠐⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠉⠀⠁⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡏⠂⡳⣀⡛⣭⠐⠏⠀⠘⠙⣿⣿⣿⣿⠏⡾⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢠⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣧⡀⠹⠃⠀⢳⣿⣿⡕⢅⡂⠀⠀⣇⠿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡇⠂⣀⡀⠀⠠⠄⣠⠞⢹⣿⣿⠍ ⣿⣿⠂⠀⠛⢿⣿⣿⣿⣿⡏⣼⣿⣿⣿⡿⣵⣿⣿⣿⣷⣯⠉⠁⠀⠀⠀⠸⣿⣿⣷⣭⣴⡀⠀⠨⡉⣧⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡄⠀⣸⣿⣃⢰⣿⣿⣾⠀⢀⠈⠀⡄⠻⠿⡐ ⣿⣿⡄⠀⠀⠨⣬⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠅⠀⠐⠠⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣀⠀⠀⢿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠗⠕⠄⠁⠀⠈⠬ ⣿⣿⣿⣆⡀⣀⡔⢊⣻⣷⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⢛⠋⡀⢂⡀⠀⠝⢉⣇⢻⣷⣄⣂⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣄⠉⢸⣿⢸⣀⠈⢻⣿⣾⣶⣾⣤⡄⠀⠀ ⣿⣿⣿⣟⢿⣿⣿⣷⣽⡟⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⡿⣣⡇⣸⡆⠀⣰⣿⠃⠹⠦⠷⡿⠞⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢻⠈⠈⢿⣿⣿⣿⣿⣿⣤⡅ ⣿⣿⣿⣿⣿⣿⣯⣭⣽⣇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣭⣿⣿⣶⣿⠋⠠⠘⣴⣞⡃⠀⠠⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣁⠀⢋⢈⢆⢶⠀⢒⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣤⣴⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠭⠉⠉⠍⠉⠉⠩⠉⠉⢀⣀⣤⣶⣿⠇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣟⠉⢿⣿⣿⣿⣿⣿⣷⣸⣿⢿⣿⡷⣄⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢡⣿⡉⡙⠉⢉⣢⠀⢂⣀⣿⣑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡀⠀⣴⢦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠨⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠑⣿⡋⠠⠛⢛⣭⠐⠎⠀⠈⠙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢠⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⡿⢟⣛⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣬⣈⠀⠀⢉⣁⠅⠀⠀⠀⢆⠾⡿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡇⠄⣀⡀⠀⠠⠄⡠⠎⢹⣿⣿⠉ ⣿⣿⠀⠀⠛⢿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢻⣭⣴⡀⠀⠨⡉⣥⣓⡆⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠘⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣮⠀⢀⠈⠀⡤⠿⠿⡀ ⣿⣿⡄⠀⠀⠨⣬⡿⢱⣿⣿⣿⣿⣿⡿⢟⣛⣛⡿⣿⡍⠛⢿⡏⠀⣾⣿⣽⣿⣦⣹⣿⣿⠁⠀⠀⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠕⠑⠄⠁⠀⠀⠬ ⣿⣿⣿⣆⡀⣀⡄⠀⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣎⠙⠀⠈⠁⠀⢹⣿⣿⣿⣿⡏⣟⠋⡀⢂⡀⠀⠙⢉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⢻⣿⣾⣶⣶⣤⡄⠀⠈ ⣿⣿⣿⣟⢛⣿⣿⢰⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠹⠦⠗⠿⠖⠀⠀⣀⣴⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡉⠫⠈⠈⢿⣿⣿⣿⣿⣷⣤⡄ ⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⢃⡀⠀⠀⠀⠈⠻⣿⣿⡿⠡⠀⣴⣞⡃⠀⠰⠀⢻⣿⣿⡌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣇⠀⢋⢀⢇⢶⠀⢲⡠⠙⣿⣿⣿⣿⣷⣬ ⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⣿⣿⣿⣷⣽⣿⣿⣿⢿⣣⣾⢁⣦⣢⡀⢼⣶⡦⣭⣤⣤⣶⣿⣿⣷⣶⣷⣶⠘⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣁⣀⣤⣶⣿⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣿⠛⠻⢿⣿⡿⢿⡿⣿⣿⣿⢿⣷⠚⢻⣷⣿⣿⣿⣿⣧⢸⣿⢿⣿⡷⣀⣹⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⡿⠛⣿⢡⣿⡉⡁⠉⢉⣠⠀⢂⣀⣿⢑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⢤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ 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⣿⡆⠠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡓⠑⣿⡋⠠⠛⢛⣭⠐⠎⠈⠸⡙⣿⣿⣿⣿⠏⡾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢻⣷⢡⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⠩⣀⠉⠈⠀⠀⢉⣙⢅⠂⠀⠀⣆⠿⣿⣿⡟⣸⠇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⢸⣿⡆⠃⣐⡀⠀⠠⠄⣠⠞⢹⣿⣿⠉ ⣿⣿⠀⠈⠛⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣷⡙⢦⣶⣶⠀⠘⢻⣭⣔⡀⠀⠨⡉⣥⣓⡇⣿⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠸⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣾⠂⢀⠨⠀⡤⡿⠿⡀ ⣿⣿⡄⠀⠀⢈⣾⣿⣵⣾⣿⣦⡙⢯⠀⠋⠀⣤⣟⣯⣭⣟⢿⣿⣿⣦⠹⣿⡄⠘⣿⣿⣿⠇⠀⠐⠠⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⢻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠵⠕⠄⠁⠁⠈⠨ ⣿⣿⣿⣆⡀⢸⢿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⣼⣿⣿⣿⣿⣷⣻⣿⣿⣧⠹⡇⢤⣞⣟⠋⡄⢂⡀⠀⡝⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢸⣀⠉⢻⣿⣴⣶⣾⣤⡄⠀⠈ ⣿⣿⣿⣟⢿⢸⡟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣊⡹⡻⠦⠷⠿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢠⣶⠉⡈⢫⠈⠈⢿⣿⣿⣿⣿⣷⣤⡅ ⣿⣿⣿⣿⣿⣇⢻⣝⡿⠿⠿⣛⠔⡀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣽⣿⣿⣿⢀⠖⠀⠳⠈⣴⣞⡃⠀⠤⠀⢻⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⠙⠻⠿⢟⣇⠀⢋⢈⢇⢦⠀⢲⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⡿⢋⣼⡯⠀⢠⣿⣜⣶⣿⣷⣾⣿⣿⣿⣿⣯⡌⣤⣤⣤⣶⣿⣿⣿⣾⣷⣶⠚⣿⣿⣿⣶⣝⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢄⣀⣤⣶⣿⠃⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠻⣿⡿⢄⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠁⢿⣿⣿⣿⣿⣿⣷⢸⣿⢿⣿⡷⣀⣻⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⢸⣿⠀⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⡿⠛⣿⢣⣿⡍⡑⠉⢉⣠⠀⢃⣀⣿⢑⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣷⢶⣼⣿⢿⣿⣿⣧⣿⣿⣷⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠃⣿⢸⣿⣿⣏⣿⣿⣿⢬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠂⠀⠀⠀⢀⠐⠁⠀⠙⡄⠈⠄⠈⠀⠴⢈⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⢾⣿⣿⠟⠛⠿⣟⠈⠛⣻⠩⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠁⠀⠀⣠⠀⠠⠁⠀⠀⠀⢀⡁⠀⠀⠀⠠⢶⠓⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡍⢀⠀⠀⠀⠸⣶⠊⢳⢦⣇⡤⣽⣿⣿⣿⣿⣿⣿⣿⣯⡉⣀⣀⠀⠛⢁⡀⠀⠀⠀⠠⠀⢠⠀⠀⠈⠈⠀⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⢳⠀⠀⠃⢀⣂⣥⣀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠬⡀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠋⠉⡀⠀⣇⣇⣡⣂⠈⣁⠀⠀⢀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⡁⢀⠀⡠⠃⠋⠂⣿⣦⣿⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⠈⠁⡀⠐⢠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣰⣦⣴⣿⣿⣿⠟⠩⠀⠀⠀⠀⠌⠂⠠⣴⠈⢁⡤⠀⠀⠀⠡⠐⣀⡅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣿⣿⣿⣶⣿⣿⡟⡜⣻⠛⠉⢉⠄⠀⠂⢹⣿⣿⣿⣿ ⠛⣀⣠⣄⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢃⢙⣻⣿⠛⠉⢛⣓⡐⠀⠠⠀⠈⢀⣠⣶⢟⡙⣤⣜⡋⠰⣀⠀⠀⠀⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⢈⠐⠁⢬⠀⠀⠘⢏⡻⠉⠁ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣯⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣴⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⣐⣀⡁⠀⠀⠀⠐⢠⣍⡃⢀⠈⠉⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡋⣉⠸⢓⣠⣿⣿⡿⢦⣬⣿⣦⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡟⠂⠀⢐⡆⠽⣿⣿⣿⣿⣦⣆⣀⡆⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⡿⣼⣿⣿⠿⠟⠻⠟⠻⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣟⣂⠀⣠⢢⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣋⣿⣿⢫⡩⠌⠉⠁⡀⠼⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡅⠀⠈⠙⢿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡊ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡆⣸⣿⣍⣠⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⢀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿ ⣿⠈⢫⣿⣿⣿⣿⣿⡿⣛⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠛⡐⢸⣿⡟⢡⣿⣯⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠐⠀⠈⣧⡩⠉⠁⠀⠀⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠠⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢫⠰⠛⢻⣭⠴⠏⠉⠩⡙⣿⣿⣿⣿⢏⣾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⡂⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⡟⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣑⢅⡂⠀⠁⣇⠿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡇⠃⣘⡀⠀⠠⠄⣠⠞⢹⣿⣿⠍ ⣿⣿⠒⠈⠛⣿⢣⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⢻⣭⣴⡀⠀⠨⣉⣧⣓⡇⣿⠂⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠘⣿⣿⡠⠀⣸⣿⣃⢰⣿⣿⣾⠂⢀⠨⠀⡤⡿⠿⡐ ⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⠅⠀⠀⠪⣿⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣄⠀⠀⣻⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣿⠵⠕⠄⠁⠁⠘⠬ ⣿⣿⣿⣆⡀⣄⡸⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣾⣟⠋⡔⢂⡀⠀⠽⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⣻⣿⣶⣶⣾⣤⡤⠀⠈ ⣿⣿⣿⣟⢿⣿⣇⠛⢁⣠⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡹⡻⠦⠟⡿⠖⠀⠀⣠⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢨⣶⠉⡘⢻⠈⠉⢿⣿⣿⣿⣿⣷⣤⡅ ⣿⣿⣿⣿⣿⣿⣿⡄⢿⣷⣂⠀⢵⣮⣋⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠳⠘⣴⣞⡃⠀⠄⠀⢿⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⣿⠟⠀⢙⠻⠿⢟⣃⠀⢋⢨⢇⢶⠁⢰⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠄⠀⠐⠛⣿⡿⢉⢇⠀⠘⣿⣿⣿⣶⣝⠉⠍⠉⠉⠉⠉⠉⠉⠉⠉⢀⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⠿⣿⣿⣿⣿⣿⡿⠒⣀⣍⣛⠛⠿⠿⠿⠿⠿⠿⠿⠛⢛⣉⡩⠄⠠⢼⣯⢶⣀⠄⠁⣜⠿⢷⣝⡀⣀⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠀⢿⣿⣿⣿⡗⣀⡴⡲⢀⠄⠀⠁⡅⠈⣹⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⢰⣶⡆⣴⣶⢲⣶⣶⣶⠀⠀⣶⣶⣶⢰⣶⣶⡆⣶⣶⣶⢰⣶⡶⠀⠀⠀ ⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡿⠛⣿⣧⣶⡍⡙⠉⠁⡢⠀⢃⠠⢿⢑⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⡏⢸⣿⣏⣀⠀⠀⣿⣿⣿⣼⣿⣿⡇⣿⣿⣀⠸⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡇⠀⠈⠙⢿⢻⣧⠀⣤⣽⢅⠀⡂⡉⠘⢛⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢻⣿⣿⣿⣧⢸⣿⣿⠛⢀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣷⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠘⠻⣿⡝⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣿⣿⣴⣿⣿⡎⠀⠛⠿⢶⣾⣆⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣶⠙⡄⣿⣿⢻⣿⢼⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⠏⠛⠿⣗⡀⠀⣠⠠⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠋⠉⠩⣁⠈⠩⠁⠉⠁⠉⢀⠁⠉⠉⠈⠩⢾⡛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣍⢀⡀⠀⠀⠸⣿⠊⠳⢦⣇⡤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣀⣀⠀⠙⢁⡀⠀⠀⠀⢠⠀⠠⠀⠀⠈⠘⠀⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⢳⠀⠀⠃⢀⣂⣵⣀⣿⣿⢿⣿⣿⣿⣿⣿⣿⠬⡀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠋⠉⡀⠀⣇⣧⣡⣂⠈⡁⠀⠀⢀⠐⡈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡁⢀⠀⡠⠃⠋⠂⣿⣦⣿⠣⣸⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⠈⠁⡀⠐⢠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣰⣦⣴⣿⣿⣿⠟⠩⠀⠀⠀⠀⠌⠂⠠⣴⠈⣁⡤⠀⠀⠈⠡⠐⢀⡅⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣷⣿⣿⣿⣶⣿⣿⡟⡜⡳⠛⠋⢉⢄⠀⠂⢹⣿⣿⣿⣿ ⠛⣀⣠⣄⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢂⢙⣻⣿⠛⠉⢋⣓⡘⠐⠠⠀⠈⢀⣠⣶⢿⡙⣬⣔⡋⠰⣀⠀⠀⠀⠠⠸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⡀⠀⠀⢈⠐⠁⢌⠀⠀⠘⢏⡻⠉⠁ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⣴⣿⣿⣿⣿⣯⣤⣤⡿⣻⡆⢉⣾⣿⢻⣿⣿⣘⣿⣶⣶⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠀⣐⣀⡉⠀⠀⠀⡐⣡⣍⡁⢀⠈⠉⡨⠁⠐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⠼⣓⣠⣿⣿⡿⣦⣼⣿⣦⣽⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡿⠆⠀⢐⡆⡹⣿⣿⣿⣿⣦⣄⣠⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⢤⣾⣿⣿⡿⣾⣿⣿⡿⠟⠻⠛⠿⣿⣿⣿⣿⡿⢿⣛⣻⣭⣽⣿⣭⣝⠛⠿⢿⣿⣿⣯⣗⣀⠀⣸⢪⢲⣿⣿⣿⣿⣿⣿⣏⣩⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣛⣽⣿⢫⡨⠌⠉⠑⡈⢸⣢⣶⣾⣿⣿⡿⣻⡽⠚⠉⠛⠻⢿⣿⣿⣿⣿⣷⡅⠀⠈⠙⢿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡊ ⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣥⠈⢹⣿⣿⡇⣴⣿⣍⣡⣴⣿⣿⣿⣿⠿⣫⣾⡁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡄⠀⢀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⢏⣄⣶⣿⣿⣿ ⣿⠀⢻⣿⣿⣿⣿⣿⡿⣛⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠿⣿⣏⠙⡐⢸⣿⡟⢡⣿⣿⣼⣿⣿⣿⣿⣿⢎⣾⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠈⣧⡩⠉⠁⠀⠄⠀⠉⠹⣴⣿⣿⣿⣿⣿ ⣿⡆⠨⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢫⠰⠛⢛⣭⠔⡏⠈⠹⡙⣿⣿⣿⣿⠏⣾⠘⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⢹⣷⢨⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿ ⣿⣿⠂⠙⣿⣿⡿⣬⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣓⢅⡂⠀⠁⣆⠿⣿⣿⡟⣸⡇⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢀⢸⣿⡇⠣⣐⡀⠀⠠⠄⣠⠟⢹⣿⣿⠍ ⣿⣿⠂⠈⠛⣿⢷⣿⣿⢷⡀⠈⠀⣀⠾⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⢻⣭⣴⡀⠀⠨⣉⣧⣓⡇⣿⠂⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⡀⡀⠀⠀⠸⣿⣿⡀⠀⣸⣿⣃⢰⣿⣿⣾⠂⢀⠨⠀⡤⡻⠿⡐ ⣿⣿⡄⠀⠀⠨⢸⣿⣿⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣿⣿⣿⠅⠀⠀⠪⣿⣿⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣭⣭⣭⣝⢢⣔⠀⠂⣿⢿⡇⢀⣿⢳⣿⢸⢿⣿⣿⣷⠗⠗⠄⠁⠁⠘⠬ ⣿⣿⣿⣆⣀⣄⡸⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣟⠋⡐⢂⡀⠀⠝⠉⣇⢻⣷⣄⣂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠿⡗⣠⣶⣶⣶⣤⠉⢸⣿⢰⣀⠈⣻⣿⣶⣶⣾⣤⣄⠀⠈ ⣿⣿⣿⣟⢿⣿⣇⠛⢁⣤⠄⠀⠐⢜⢿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡇⢈⡹⡻⠮⠷⡿⠖⠀⠀⣀⣶⡌⣿⣿⣿⣿⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⢏⡀⠀⣿⣿⣿⣿⣿⢨⣶⠉⡙⢫⠈⠉⢿⣿⣿⣿⣿⣿⣠⡅ ⣿⣿⣿⣿⣿⣿⣿⡀⢿⣯⣂⠀⢴⣮⣋⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠳⠘⣴⣞⡃⠀⠤⠀⢿⣿⣿⣌⢿⣿⣿⣿⣿⣿⣮⣛⣿⣿⣿⣛⣿⡿⠟⠀⢙⠻⠿⢟⣇⠀⢋⢨⢇⢦⠀⢰⡠⠙⣿⣿⣿⣿⣷⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠄⠀⠐⠛⣿⡿⢉⣇⢀⠘⣿⣿⣿⣶⣝⠩⠉⠉⠉⠉⠉⠩⠉⠉⠉⢀⣀⣤⣶⣿⠇⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⣿⡿⠿⣿⣿⣿⣿⣿⡿⠒⣀⣍⣛⠛⠿⠿⠿⠿⠿⠿⠿⠛⣛⣉⡩⠄⠠⠼⣮⢶⡀⠄⠁⣜⠿⢷⢝⡀⣀⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠀⢿⣿⣿⣿⡟⡀⡴⡢⢂⠀⠀⠡⡍⠈⣹⡾⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⢰⣶⡆⣴⣶⢲⣶⣶⣶⠀⠀⣶⣶⣶⢰⣶⣶⡆⣶⣶⣶⢰⣶⡶⠀⠀⠀ ⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡿⠛⣿⣣⣶⡍⡝⠉⢩⡢⠀⢃⠠⢿⢑⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣷⣿⡏⢸⣿⣏⣀⠀⠀⣿⣿⣿⣼⣿⣿⡇⣿⣿⣀⠸⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡇⠀⠈⠙⢿⢻⣧⠀⣤⣿⣅⠀⡂⡉⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⢸⣿⣿⠛⢀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣷⣾⣿⣿ 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⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠨⠜⠿⠟⢷⣹⣯⢼⣹⣿⣿⣿⣵⠄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠻⠥⢦⣼⣅⢻⡞⣹⣿⣿⢿⣿⣿⣿⣿⡄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣽⣿⣮⣷⣜⣻⠮⣻⡟⠫⢿⣿⠟ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⢀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠀⢱⣣⣴⢰⢿⣷ ⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢈⣀⣀⣉⣁⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣼⡣⡨⢛⣿⣿⣿⣿⣿⣿⠩⣿⣿⣉⣯⣼⣦⢠⡘⠛⠋⠁⠀⡡ ⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣀⣿⣇⢽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣶⣴⢼⢿⢦⠅ ⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣴⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⡉⠻⢿⣿⣿⢙⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇ ⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣷⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡋⣀⣼⣿⣿⣳⣟⢻⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣗ ⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣷⣿⣿⣶⣿⠻⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧ ⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠫⠛⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣌⠙⢦⡀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣯⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀ 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⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢠⠜⠿⠿⢗⡽⡭⢼⣹⣿⣿⣿⣵⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠻⡅⢢⣴⣅⢳⡞⣱⣿⣿⢿⣿⣿⣿⣿⡆ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣮⣷⣜⣿⠮⣺⡟⣫⡿⣿⠟ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡄⠀⢡⣦⣴⢰⢷⣷ ⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢈⣀⣀⣉⣉⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣸⡃⡨⠛⣿⣿⣿⣿⣿⣿⠉⣿⣯⣈⣯⣼⣇⢠⡘⠙⢋⠁⠀⠠ ⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣐⣿⣗⢽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣶⡴⢾⢿⣦⠁ ⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⢃⣿⣿⣿⣿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣬⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⡉⠻⢿⣿⣿⠝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇ ⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣷⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡏⣀⣼⣿⣿⣻⣟⢻⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷ ⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣷⣿⣷⣶⣿⠻⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠊⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣷⣤⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣿⢹⣿⢸⣿⣿⣿⡟⢿⣿⣼⣿⣟⣿⣿⣼⣿⣿⣶⠀⠀⣿⣿⢸⣿⢸⣿⡇⣿⣿⣶⣦⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⠊⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣵⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⢾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠙⣿⣿⠛⠙⠉⠙⠄⢿⣛⣙⡕⣮⡿⠟⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠘⣿⣿⣦⡀⠀⠀⠘⠛⠛⠳⠮⠸⠐⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠏⣼⡿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠹⣺⣿⡥⢀⠠⠀⢶⣠⠀⠀⠈⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣰⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⣿⡄⠰⠧⠀⠀⢀⣀⣐⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⢾⡟⢚⣷⣆⣈⣙⠸⢇⣷⡄⢶⡄⢺⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⡼⣧⣾⣾⣧⢛⣭⡣⠚⡿⣿⢾⣿⣿⣿⡟⣈⣿⣿⣿⣿⣿⣿⠇ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢢⠜⠿⠿⢗⡹⡯⢼⣹⣿⣿⣿⣵⠆ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠻⡅⢢⣴⣥⢳⡞⢱⣿⣿⢿⣿⣿⣿⣿⡄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣮⣷⣜⣿⠮⣻⡟⢻⡿⣿⠟ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⢀⣾⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣄⠀⢡⣦⣤⢰⢿⣷ ⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢈⣀⣀⣉⣁⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣸⡇⡨⢛⣿⣿⣿⣿⣿⣿⠉⣿⣿⣉⣿⣼⡆⢠⡚⠙⢋⠁⠀⠠ ⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣰⣿⣅⢽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣶⡴⢾⢿⣦⠅ ⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣼⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⡉⠻⢿⣿⣿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇ ⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣷⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡏⣁⣼⣿⣿⣻⣟⢻⢏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷ ⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣷⣿⣿⣶⣿⠿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠊⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣌⠙⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀ 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⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣽⣹⣿⣿⣿⣵⡎ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢌⣀⣀⣉⣁⠀⠀⠘⠻⠟⠁⢸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣥⡧ ⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠐⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽⢾⣿⣷⡇ ⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⢿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⣹⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷ ⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀ 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⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣵⠇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣴⡀⠀⠀⢌⣁⣀⣉⣉⠀⠀⠘⠻⠿⠁⢸⣿⣿⡇⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣦⡧ ⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠐⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢾⣿⣷⡇ ⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⣹⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡆⣰⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀ 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⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣵⠇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠐⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢜⣁⣀⣉⣉⠀⠀⠘⠻⠟⠁⢸⣿⣿⡇⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣦⡧ ⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢾⣿⣷⡇ ⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣾⣿⡌⠉⣈⣻⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⡆⣴⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣯⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀ 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⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣵⠇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡟⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⡄ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠐⠀⠀⢸⣿⣿⡟⣼⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣌⠙⢷⣦⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣿⣿⡿⢀⣿⣿⡇⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣷⣤⡀⠀⠀⢌⣁⣀⣉⣉⠀⠀⠘⠻⠟⠁⢸⣿⣿⡇⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣦⡧ ⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣽⢾⣿⣷⡇ ⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠃⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣾⣿⡌⠉⣈⣻⣿⣿⣿⣿⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠇⣰⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣦⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⣫⣵⣿⣿⣿⡿⠃⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⡆⣴⣶⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⡿⠿⠟⠛⠁⠀⠀⠀⣀⣤⣤⣤⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣙⠻⠿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣌⠛⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⣿⣏⣿⣿⢸⣿⣿⣿⣇⢸⣿⣿⠛⠀⠀⣿⣿⣿⣿⢿⣿⡇⣿⣿⠛⠀⣿⡇⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢭⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣾⢙⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⢿⣷⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣻⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷⡀⠻⣾⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⢷⣆⠘⢿⣿⣮⣻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣧⡘⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡦⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⠈⢻⣶⣿⣿⣦⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⡇⠀⠐⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣭⣿⣿⣿⣿⠁⠀⠀⣰⡸⠿⣿⣾⣻⣿⣿⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⡄⠀⠀⣽⠟⢡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣷⣿⣽⣟⢿⣿⠀⢺⣿⣿⣿⣿⣿⣿⡇⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠔⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⡇⠀⠀⠈⠛⠉⠉⡉⣽⣟⣓⣋⣱⣾⣿⣿⣿⣿⣿⡹⣷⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡠⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣛⣿⡃⠀⠀⠀⠀⠀⠀⠈⣿⡿⡿⠻⣠⣽⣿⣿⠿⣿⣿⣷⡘⣿⡌⣿⣿⣿⣿⣿⣻⢛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠀⠀⢸⣷⢀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⡁⠀⠀⠀⠀⠀⠀⠘⢃⠌⢐⣱⡟⣿⣿⣸⣿⣿⣯⣿⣧⣾⣶⣾⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⡇⠀⣾⠟⢠⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⠀⠋⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠁⠀⢀⡀⣀⣄⣶⢼⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠙⠛⠛⠻⠟⢛⣻⢟⠿⢿⣿⣿⠿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⠿⢆⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣤⣄⡀⠈⠉⠉⠀⠀⠉⢭⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠋⠻⣿⣿⡛⠿⠯⠛⣿⣿⣫⣟⡁⠀⣠⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠃⣈⡉⣠⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠙⣛⡛⠇⠻⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣿⣿ ⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢁⠀⠀⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣤⣆⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⣀⠐⣿⣟⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠁⠀⣹⡿⠆⣀⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⢠⣿⣷⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀ ⠀⢣⣀⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠧⠟⣛⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⠀⠀ ⠀⠀⣽⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣤⠤⣒⠈⠀⠀⠐⠋⠛⠛⢛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣢⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⡿⠿⠿⠟⠛⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 6031 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/18/phoronix86-amd/#comments Gemini version at gemini://gemini.techrights.org/2022/02/18/phoronix86-amd/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ When_AMD_Sends_You_a_Crate_of_CPUs_Worth_(Market_Value_of)_Roughly_$500,000⠀✐ Posted in Deception, Hardware, Marketing at 4:41 pm by Dr. Roy Schestowitz Recent: When_Blogs_Become_Marketing_and_Benchmarks_Become_Product_Promotions Front_page of Phoronix moments ago (screenshots minutes old): 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇AMD_at_phoronix_front_page⦈_ Number of employees at Intel: 121,100 (2021) Number of employees at AMD: 15,500 (2021) Summary: The apparent bias or the priorities at Phoronix seem to have changed (no explanation was ever provided for the ‘gifts’); a single job opening at AMD, for instance, now merits a “news” post and anything that’s not x86 is mostly ignored as if it’s only a Wintel world ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠚⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣭⣉⣽⣬⣉⣍⣍⣽⣌⣩⣉⣷⣮⣍⣏⣩⣍⣼⣿⣿⣿⣿ ⣿⣿⣏⣀⣀⣸⣭⡭⢭⠽⠭⠯⠍⠭⠭⣭⣿⣽⣭⣽⣭⣽⣽⣽⣯⣭⣧⣭⣿⣬⣽⣏⣯⣧⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣭⣭⣯⣭⣭⣭⣿⣯⣹⣽⣽⣭⣭⣭⣯⣿⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠐⠲⡆⠐⠒⠶⣦⠀⠈⣿⠶⠾⠶⠿⠿⡷⠴⠼⢷⠿⠧⠿⠷⡶⠶⠾⠷⠿⠷⡶⠶⡿⣿⢿⡿⠿⠿⠿⠿⠿⢿⠿⢿⠿⠿⣿⣿⣿⡇⣿⢷⠾⠷⡶⡶⠾⠶⠶⣾⡾⢶⣷⣷⣾⣶⣷⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣓⣛⣛⡒⣺⣒⣳⣿⣶⣿⣿⣷⣿⣿⣿⣷⣿⣷⣷⣾⣷⣷⣷⣿⣿⣷⣿⣿⣿⣾⣿⣾⣿⣾⣿⣿⣿⡇⣿⣻⣛⣛⣻⣛⣻⣟⣻⣻⣟⣛⣻⣛⣛⣿⣛⣟⣛⣿⣿⣿⣿ ⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣭⣭⣭⣯⣯⣽⣽⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡾⡼⠼⠿⣿⠶⠮⠷⡴⣿⡾⠵⢷⠽⠮⠷⠴⠾⣷⣤⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣛⣛⣛⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⠛⠛⢻⢟⠟⠛⠻⡟⠛⢛⠛⣻⢻⢟⣻⡛⠛⢿⠛⣻⠛⡟⠟⡻⡟⢛⡻⢻⡟⠿⠛⢻⢛⢻⠛⢻⡟⡟⡟⡟⠛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣩⣏⣍⣯⣛⣋⣟⣹⣛⣟⣻⣙⣛⣟⣻⣛⣉⣟⣹⣿⣿⣿ ⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣝⣛⣛⣛⣻⣏⣛⣛⣻⣏⣛⣻⣙⣙⣻⣿⣉⣏⣛⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣤⣶⢿⣾⢴⡾⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠤⠤⠯⠤⠬⡽⠴⠤⠤⠤⠥⢬⠤⠯⠤⠤⠤⡤⠯⡭⠼⡤⠤⡯⠭⠤⠦⡧⠼⡤⡼⠤⡥⠽⠿⠿⣿⣿⡇⣿⠖⠶⢒⢳⣿⢷⠳⢲⡲⢶⠶⠲⡻⢷⢶⣶⣶⣶⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣒⡒⣒⣚⣖⣓⣒⣓⡓⣲⣓⣚⣚⣒⣖⣒⣓⣳⣓⣓⣲⣓⣓⣓⡒⣞⣒⡓⣓⣳⣓⣒⣓⡚⡓⣾⣿⣿⡇⣟⣛⣋⣿⣛⣛⣛⣛⣛⣻⣛⣻⣟⣛⣛⣛⣟⣻⣛⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣬⣭⣽⣭⣭⣭⣭⢭⡭⡭⣭⣭⡭⣭⣯⣯⣭⣯⣭⡭⣭⢽⣭⣭⣭⣭⣯⣭⣹⣭⣭⢽⣭⣽⣭⣽⣿⡇⣿⡬⢬⣥⣯⣭⣼⣭⣭⣽⣽⣧⣧⣭⣯⣭⣥⣤⣤⣵⣾⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠚⠒⢒⢲⠒⠒⢶⣷⣶⣾⣶⣶⣶⣶⣶⣷⣷⣾⣾⣶⣾⣾⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣿⣿⣿⡇⣿⠾⠶⠿⠿⠿⢿⡿⡿⠿⠿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣛⣛⣟⣛⣛⣿⣻⣛⣛⣛⣻⣉⣉⣿⣛⣛⣿⣛⣟⣛⣻⣿ ⣿⣿⡿⣿⣿⣿⡿⡿⡿⡿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⡿⣿⣿⢿⢿⠿⠿⢿⠿⠿⡿⢿⡿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡇⣿⣭⣭⣭⣭⣭⣯⣭⣽⣯⣯⣭⣭⣭⣿⣭⣭⣯⣯⣭⣻⣿⣿ ⣿⣿⡷⠷⣾⠷⣷⣷⢶⣿⣾⣷⣶⣾⣶⣿⣷⣶⣶⣵⣾⣾⣷⣶⣿⣷⣿⣷⣶⣶⣾⣶⣶⣶⣾⣾⣿⣷⣶⣿⣷⣶⣶⣶⣷⣷⣶⣿⣷⣾⣶⣿⣿⣿⡇⣿⣶⣦⡶⡶⣶⣷⢾⢶⣶⣷⣾⡶⣶⢶⣶⣷⣶⣾⢿⣿⣿⣿ ⣿⣿⣿⠛⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⣿⡿⠿⠿⠿⠿⢿⠿⠿⣿⠿⢿⠿⠿⠿⠿⠿⣿⠿⠿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠳⣚⣿⣷⣿⣿⣾⣶⣶⣶⣶⣷⣾⣿⣾⣷⣶⣶⣾⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣋⣛⣛⣉⣉⣉⣽⣛⣻⣛⣛⣛⣛⣛⣛⣻⣛⣙⣛⣟⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣙⣏⣛⣛⣿⣿⣿⡇⣟⣋⣉⣿⣛⣛⣟⣻⣙⣻⣻⣻⣻⣟⣛⣛⣛⣛⣛⣻⣻⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠥⠬⠤⠽⠭⠭⠽⠴⠥⡬⠭⠭⠧⠭⠯⠽⠭⠥⠭⢧⠴⠭⠬⠭⢯⠯⡭⠭⠭⠭⠽⢤⠤⡭⢭⣿⣿⣿⡇⣿⢽⣭⣯⣯⣮⣤⠶⣯⣭⢽⣮⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣚⣒⣒⣒⣗⣒⣒⣒⣒⣓⣖⣒⣒⣒⣒⣒⡛⣚⣒⣾⣚⣲⣒⣒⢞⣒⣓⣒⣖⣒⣲⣚⣒⣒⣚⣛⣿⣿⡇⣿⣶⣴⣶⣶⣷⣶⣿⣶⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢾⡶⠶⢶⡷⢦⠶⠷⣾⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣶⣿⣿ ⣿⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣻⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣭⣿⣯⣽⣭⣍⣯⣭⣹⣭⣽⣭⣍⣽⣽⣽⣽⣿⣽⣿⣿ ⣿⣿⣧⢴⠧⠷⢥⡧⠼⡽⢤⠯⠮⣥⣯⣧⣽⢯⣼⣤⣧⣤⣷⡼⣿⣽⠬⡥⢧⣥⢧⣷⣥⢷⣤⣶⣶⣤⣯⣦⣤⣿⣮⣾⣴⣧⣴⣽⣿⣿⣿⣿⣿⣿⡇⣿⠶⠷⠿⠶⠷⢾⣶⣶⣶⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⡎⢹⠉⠉⢹⢹⢹⣿⣿⣿⣿⠻⠒⢒⢲⠒⡟⠲⢲⢓⠒⡒⠳⠚⠲⢚⠶⠞⢻⠗⠒⢓⡟⠛⠛⢿⠛⡛⡛⡿⠻⠿⠛⡛⡿⠟⠟⣿⣿⡇⣿⢻⢻⢿⣿⣿⢿⠻⣿⠿⢿⠻⢿⠿⢿⠻⠟⢿⠿⠿⡿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣏⣭⣭⣩⣏⣭⣭⣭⣻⣭⣉⣍⣭⣉⣭⣩⣽⣭⣩⣩⣍⣭⣭⣉⣹⣍⣍⣏⣩⣹⣽⣭⣹⣭⣭⣽⣿⡇⣿⣟⣏⣭⣉⣛⣙⣫⣻⣟⣟⣏⣉⣹⣙⣛⣛⣏⣽⣿⣿⣿⣿ ⣿⣿⣷⣾⣷⣶⣶⣶⣾⣶⣷⣶⣶⣼⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣶⠶⠶⠿⠿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢛⠟⠻⡟⠿⡿⢿⢿⡻⠿⢿⠻⢛⢿⡿⡟⠿⠿⣿⣿⣿⣿ ⣿⣿⣧⠤⠤⠼⠽⠦⠴⠯⠵⠤⠴⠦⠾⣮⣤⢵⣴⣯⣶⣥⢼⣬⣴⣾⣤⢧⢤⢶⣴⡼⣤⣼⣷⣥⣶⢴⣧⣴⡼⣤⣧⣼⣦⣷⣼⣮⣶⣤⣴⣼⣿⣿⡇⣿⣯⣹⣙⣯⣍⣹⣝⣭⣻⣽⣿⣏⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⠓⢒⠚⡖⠟⡓⡖⠚⠻⠚⠚⢺⠚⠚⣳⠒⠛⠛⠛⠚⡖⠗⠓⠓⠛⠻⠛⠛⠟⡟⢛⠟⠛⡟⠛⣿⣿⡇⣿⡷⠶⠶⠶⠷⠷⣷⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣩⣭⣭⣹⣩⣭⣏⣭⣩⣭⣯⣭⣍⣭⣻⣭⣭⣭⣭⣩⣭⣍⣏⣩⣽⣭⣭⣩⣯⣭⣭⣹⣿⣿⣿⣿⣿⡇⡿⠛⠛⣿⠿⠛⠿⠟⠿⢟⣿⢿⣛⠿⠿⠛⠿⢿⠻⣿⣿⣿⣿ ⣿⣿⡿⠿⠿⡿⠿⢿⠿⠛⠻⠿⠿⠿⠿⡿⠶⠖⠰⠶⠲⢶⠶⠶⡶⠷⠲⠖⡖⠶⠆⠶⠾⢾⡷⡶⡔⠞⢷⠶⠦⠗⠷⠶⠶⢼⠾⠲⡶⠶⠶⣶⣿⣿⡇⣿⣉⣍⣫⣏⣭⣽⣻⣟⣽⣿⣯⣯⣽⣟⣽⣏⣉⣩⣿⣻⣿⣿ ⣿⣿⣟⣛⣛⣻⣙⣉⣉⣛⣏⣹⣙⣟⣝⣙⣏⣉⣏⣋⣉⣟⣙⣹⣋⣹⣙⣛⣏⣛⣛⣛⣛⣉⣉⣏⣙⣏⣋⣍⣏⣉⣉⣛⣉⣝⣹⣉⣹⣋⣉⣛⣿⣿⡇⣿⠷⠾⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣧⣦⣴⣤⣼⣴⣼⣤⣤⣤⣦⣼⣶⣤⣬⣤⣼⣴⣤⣤⣴⣤⣤⣤⣧⣤⣴⣤⣼⣴⣴⣼⣤⣤⣦⣮⣧⣤⣦⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 6107 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_18/2/2022:_EasyOS_3.4.1_Soon,_Media_Conflating_Snap_With_‘Linux’⠀✐ Posted in News_Roundup at 6:17 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ 7_New_Features_to_Try_in_Kali_Linux_2022.1⠀⇛ For years, cybersecurity-centric Linux distributions have been revolutionizing penetration testing and security auditing for internal and remote networks. Offensive Security, Kali Linux’s developers, gives you the first major release of 2022 with its newest version. Kali 2022.1 is packed to the brim with innovations and the latest feature additions, making it a power-packed distro for the new year. Here are some exciting new features of Kali Linux 2022.1 you need to try right now. # ⚓ The_7_Best_Linux_Docks_to_Give_Your_Desktop_a_New_Look⠀⇛ Is your Linux desktop cluttered with apps, and you struggle to find an app every time you want to launch it? Well, it turns out, you can use a dock to fix this. Generally speaking, an application dock is a system component on certain desktop operating systems that facilitates multitasking by providing quick access to apps and utilities. Not only that, but it also contributes to the visual appearance of your desktop, making it both functional and appealing. On Linux, there are a variety of apps you can use to get a dock on your desktop. Let’s check out some of these best docks apps for Linux. # ⚓ Dell_Latitude_3510_Laptop_10th_Generation_Intel_Core_i5- 10210U/4GB/1TB_HDD/Ubuntu [Ed: Only noteworthy because Dell offers GNU/Linux in India]⠀⇛ Planning to buy a new laptop with exceptional features and specifications? Dell Latitude 3510 Laptop 10th Generation Intel Core i5-10210U/4GB/1TB HDD/Ubuntu is a good choice that you can go for. The laptop is equipped with a 10th Generation Intel Core i5-10210U with 1.6 GHz clock speed that lets you multitask with ease and experience faster performance [...] You can purchase this Dell Latitude 3510 Laptop 10th Generation Intel Core i5-10210U/4GB/1TB HDD/ Ubuntu in India at Rs 53,969. Also, you will get a warranty of 1 Year on it from the manufacturer from the date of purchase. # ⚓ macOS_vs._Windows_vs._Linux:_Which_OS_Would_You_Buy [Ed: Very poorly written and poorly researched, maybe machine- generated]⠀⇛ o § Audiocasts/Shows⠀➾ # ⚓ Built_to_impress:_but_does_the_SLIMBOOK_TITAN_live_up_its COLOSSAL_name?_–_Invidious⠀⇛ Thanks to Slimbook for sending us this unit. Overall, Ethan and I were quite impressed with this machine and we really like it. o § Applications⠀➾ # ⚓ Flatpak_App_of_the_Week:_Minder_–_Powerful_Mind_Mapping Software_to_Visualize_Your_Ideas⠀⇛ With Minder you will be able to easily and quickly create visual mind-maps thanks to an automatic layout system and the plethora of tree layouts to choose from. You can add images and tasks to nodes, create node-to-node connections with optional text and notes, add stickers and node groups, as well as to stylize nodes, links, and connections, or colorize node branches. The interface is quite simple and intuitive featuring tabs so you can open multiple mindmaps, quick search of nodes, as well as connection titles and notes, zoom in and out, undo and redo changes, as well as a Focus Mode to focus on certain ideas and to better view and understand portions of your mind-map. # ⚓ GStreamer_1.20:_Embedded_&_WebRTC_lead_the_way⠀⇛ Made available earlier this month, GStreamer 1.20 is the fruitful result of 17 months of hard work from the entire community. Over 250 developers contributed code to make this release happen, and once again, Collabora had more contributors than any other organization. Our work focused on the two areas in which we believe GStreamer shines the brightest: embedded systems, and network streaming, in particular WebRTC. Below is a summary of the impact our team of engineers had on this latest release. As usual, you can also learn more about the enhancements done by the rest of the community by looking at the project’s 1.20 release notes. o § Instructionals/Technical⠀➾ # ⚓ Three_Examples_to_Increase_Request_Timeout_in_NGINX_– LinuxCapable⠀⇛ NGINX is one of the best choices for serving long- running requests because it has a robust architecture. However, you might need to increase your request timeout to ensure that NGINX can easily handle these heavy loads. By default, it is set at 60 seconds, but if you cannot serve your entire traffic without hitting this limit, try raising it higher, like 75 or 100 milliseconds (or whatever makes sense for how busy the site is). The error “504: Gateway Timeout” will appear if there are not enough resources available on the host machine; however, using some proxy timeout settings should fix these problems – including read/connect delays as well as sending messages alone; before waiting till everyone sends them back! In the following tutorial, you will learn how to increase request timeout in NGINX using proxy_read_timeout, proxy_connect_timeout, proxy_send_timeout directives to fix 504 Gateway Timeout error. # ⚓ How_to_Install_Jitsi_Meet_on_Ubuntu_–_OSNote⠀⇛ Jitsi Meet is a WebRTC-based video conferencing software that allows you to communicate with others. A Jitsi Meet server allows you to join multi-person video conference rooms that function similarly to a Zoom or Skype meeting. The advantage of a Jitsi conference is that all of your data travels only through your server, and end-to-end TLS is used to secure the connection. # ⚓ New_Linux_User?_7_Tips_to_Help_You_Excel_at_Using_the_OS_– LinuxBuz⠀⇛ Long-time Windows or Mac users may find it difficult to shift to Linux, and in most cases, it’s only due to the professional necessities. So, here in this article, we will make it easier for you to understand Linux in much easier ways so that you can explore more. If you are not a power user, spend some time learning from scratch to grab the little things that can prove to be helpful in the later stage. The more you use it, the more you learn, and the more you get into it. # ⚓ How_to_Install_FastPanel_on_Ubuntu_–_VITUX⠀⇛ Fastpanel is a web-hosting control panel. It provides web-based intuitive, point-and-click interfaces for common tasks such as transferring files, installing applications, updating PHP versions, and creating email accounts. Fastpanel is written in PHP5, uses the PEAR DB database layer, and includes over 100 database functions (including MySQL-specific functions such as “orelse” or “bcp”) as well as a large number of other useful functions (including file management, image conversion, HTTP authentication, and session handling). Fastpanel is compatible with all major web servers on Unix/Linux platforms: Apache 1.3+, Nginx 0.7+, and Lighttpd 1.5+. Have you ever wanted to install FastPanel on Ubuntu? Have you been scared to try it because you thought it would be a huge pain to get started? We’ve done all the hard work for you. Read this guide, then follow along, step by step. In no time, FastPanel will be up and running on your Ubuntu server in minutes. # ⚓ Install_Varnish_7_for_Nginx_on_Rocky_Linux_8⠀⇛ Varnish cache is a free and open-source cache accelerator used to speed up your website by caching the content in memory. It is extremely fast and reduces the page load time, which helps with your SERPs and improves user experience. It is used by many organizations including Facebook, Twitter, and Wikipedia. Varnish sits between Nginx and clients that receive requests from clients and forwards them to the backend. This will improve the webserver performance because Varnish will serve content from memory. In this tutorial, I will show you how to install Varnish 7 for Nginx on Rocky Linux 8. # ⚓ How_To_Install_LibreOffice_on_AlmaLinux_8_–_idroot⠀⇛ In this tutorial, we will show you how to install LibreOffice on AlmaLinux 8. For those of you who didn’t know, LibreOffice is a free and open-source office suite and is often considered a good alternative to the Microsoft Office suite. LibreOffice includes Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector graphics and flowcharts), Base (databases), and Math (formula editing). This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of LibreOffice’s free open-source office productivity suite on AlmaLinux 8. You can follow the same instructions for CentOS and Rocky Linux. # ⚓ How_To_Install_OpenRGB_on_Ubuntu_20.04_LTS_–_idroot⠀⇛ In this tutorial, we will show you how to install OpenRGB on Ubuntu 20.04 LTS. For those of you who didn’t know, OpenRGB is free and open-source software used to control RGB lighting control that does not require manufacturer software. The project is focused to provide support for multiple hardware manufacturers’ products to reduce the programs load, which is limited to Windows, superfluous. OpenRGB supports ASUS, ASRock, Corsair, G.Skill, Gigabyte, HyperX, MSI, Razer, ThermalTake, and more This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you the step-by-step installation of OpenRGB software for controlling RGB lighting on Ubuntu 20.04 (Focal Fossa). You can follow the same instructions for Ubuntu 18.04, 16.04, and any other Debian-based distribution like Linux Mint. # ⚓ How_to_Install_MERN_Stack_with_Nginx_on_Debian_11⠀⇛ How to install MERN stack with Nginx on Debian 11. MERN stack is a setup with MongoDB, Express, React and Node.js. This is one of the variants of MEAN stack. MongoDB is the database, Express with Node.js is used for backend which communicates with the database, React is the client side or frontend. We will use Nginx reverse proxy to Node.js server and setup Let’sEncrypt SSL. In this guide you are going to learn how to setup MERN stack on your Debian 11 server. This setup is tested on Google Cloud, so it should work fine on other VPS, cloud servers running Debian 11. # ⚓ Simple_Way_To_Disable_The_Screen_Lock_On_Your_Ubuntu 21.10⠀⇛ In this tutorial we are going to show you how to disable the screen lock on your Ubuntu 21.01 desktop environment using the settings panel. What is lock screen and what are the benefits of having or not having it on? The lock screen option is mainly used by the user when he needs to secure his computer system with a password. The lock screen can lock the screen after user inactivity for a period of time like the default 5 minutes on the Ubuntu desktop environment or by pressing the windows button and L. # ⚓ Add,_switch,_delete,_and_manage_Linux_users_in_KDE_| Opensource.com⠀⇛ Sharing a computer in a household is usually a pretty casual affair. When you need the computer, you pick it up and start using it. It’s simple in theory, and mostly works. That is, until you accidentally grab the common computer and accidentally post screenshots of your server’s uptime to your partner’s cooking blog. Then it’s time for separate user accounts. From the very beginning, Linux has been a multi- user system. It’s designed to treat each user, so long as they log in, as a unique human being, with a desktop all their own, a unique web browser profile, access to their own documents and files, and so on. The KDE Plasma Desktop does a lot to make it easy to switch from one account to another, but first you must set up a user account for each person who you expect to use a computer. You might also set up a special account for guests (I call this account, pragmatically, guest.) # ⚓ Install/Upgrade_MariaDB_10.8_on_Ubuntu_20.04_LTS_– LinuxCapable⠀⇛ MariaDB is one of the most popular open-source databases next to its originator MySQL. The original creators of MySQL developed MariaDB in response to fears that MySQL would suddenly become a paid service due to Oracle acquiring it in 2010. With its history of doing similar tactics, the developers behind MariaDB have promised to keep it open source and free from such fears as what has happened to MySQL. MariaDB has become just as popular as MySQL with developers, with features such as advanced clustering with Galera Cluster 4, faster cache/ indexes, storage engines, and features/extensions that you won’t find in MySQL. In the following tutorial, you will learn how to install or upgrade MariaDB 10.8 on Ubuntu 20.04 LTS. # ⚓ 6_steps_for_migrating_a_PostgreSQL_database_between containers_|_Enable_Sysadmin⠀⇛ I decided to run Kanboard, an open source project management application, in a rootless Podman pod as a small weekend project. The pod consists of three containers, an infra-container, a kanboard- container, and a postgresql-container. That deployment went well, but eventually, the image I used for the postgresql-container became deprecated, meaning it was no longer receiving updates. It was time to move to a different image, but that meant migrating a database between containers. It sounds intimidating, but the process is actually straightforward. Here’s how to do it. # ⚓ Install_Microsoft_Fonts_on_Linux_Mint_20_LTS_– LinuxCapable⠀⇛ Most Linux Distributions use open-source fonts to substitute Microsoft’s iconic typefaces like Arial, Courier New, and Times. Red Hat created the Liberation family to replace these similar-looking but different sizes — all you have to do is select your preferred font when editing documents so that they’ll be readable without any disruptions! For users who want to install Microsoft fonts and want the option to use them in LibreOffice, the following tutorial will teach you how to install Microsoft fonts on Linux Mint 20 LTS. # ⚓ How_To_Install_Akaunting_on_Debian_11_–_idroot⠀⇛ In this tutorial, we will show you how to install Akaunting on Debian 11. For those of you who didn’t know, Akaunting is a free, open-source, and online accounting software for small businesses and freelancers. Akaunting provides an elegant and intuitive UI will all the features and controls needed to stay abreast of your cashflows and transactions. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of Akaunting open-source accounting software on a Debian 11 (Bullseye). # ⚓ How_to_Install_FFmpeg_5.0_in_Ubuntu_20.04_or_Ubuntu_18.04 via_PPA_|_UbuntuHandbook⠀⇛ The popular FFmpeg multi-media library released version 5.0 recently. Here’s how to install it in Ubuntu 20.04, Ubuntu 18.04 and/or Ubuntu 16.04 via PPA. # ⚓ How_to_install_Kali_Linux_2022.1_overview_–_Invidious⠀⇛ In this video, I am going to show how to install Kali Linux 2022.1 overview. # ⚓ How_to_install_ONLYOFFICE_Desktop_Editors_on_Zorin_OS⠀⇛ ONLYOFFICE desktop app is an open-source office suite pack that comprises editors for text documents, spreadsheets, presentations, and forms. Along with offline work, it’s possible to connect the application to the cloud for online document collaboration. The source code of the suite is available on GitHub under the AGPL v.3.0 license. # ⚓ How_to_Install_PHP_7.4_on_CentOS_8_|_RHEL_8_–_Unix⠀⇛ PHP is a general-purpose scripting language geared towards web development. The PHP reference implementation is now produced by The PHP Group. PHP originally stood for Personal Home Page, but it now stands for the recursive initialism # ⚓ Workstation_Failed_Install_on_Ubuntu/CentOS/RHEL_(VMware Kernel_Module_Updater_fails)⠀⇛ Hi Guys, Sometimes you may have a trouble completing the VMware Installation on a newly installed Ubuntu or RHEL or even CentOS. # ⚓ dbus_daemon_fails_with_undefined_symbol:_XML_SetHashSalt FiX⠀⇛ To be honest, i was busy with this issue for 2 days. I have googled everywhere and tried all the suggested solutions, but nothing works. While the system boots, it still hanging with start D-bus messages. It takes too long to reach the console, but even with that, you will not be able to log in with LDAP or ssh Clients. All services using the Dbus are down. The Only Way is to use Rescue mode to handle this issue quickly. # ⚓ How_to_manage_users_in_Zorin_OS_–_Real_Linux_User⠀⇛ Probably for most people their computer is literally their personal computer. These days lots of children have their own computers, but what if you have one family computer that is being shared by multiple persons. If you allow everyone within the family to use the same account, you can for sure expect problems. There will be chaos in the structure of system and personal files, there will be an abundance of apps installed by different people with different interests, and there will be a great chance that family members mutate or delete each other’s files without being aware of the consequences for others in your household. And maybe worse, with a single user setup, the young kids also have the freedom to use the computer when you are not around. In Zorin OS, just like in any other serious desktop operating system, it is possible to create multiple user accounts. And it is advisable to use it. In this tutorial I will explain how to manage users in Zorin OS. # ⚓ How_To_Install_Virtualmin_on_CentOS_8_/_RHEL_8⠀⇛ Virtualmin is a domain hosting and website control panel which gives the ability to create and manage many domains, as well as simplify both automation and tasks. It is based on Webmin. Virtualmin is an alternative to cPanel and Plesk Virtualmin is available in two versions. Virtualmin GPL and Virtualmin Professional. The Virtualmin GPL version is fully free and open-source software and does not require monthly fee, compared to the Virtualmin Professional version which requires a monthly or annual fee. # ⚓ Adam_Young:_Root_versus_groups⠀⇛ If you lock down everything, you either need to hand out keys, or plan on doing everything yourself, and getting overwhelmed. Probably the single most power ful tool in Linux land to keep people from having to be “root” is the group concept. For example, if I want people to run Docker containers, they need to be able to talk to the Docker socket. The root user can do this by virtue of its global access. However, the more limited access approach is to add a user to the docker group. o § Games⠀➾ # ⚓ Proton_Experimental_heats_up_with_fixes_coming,_plus_a_disk space_saving_measure_|_GamingOnLinux⠀⇛ Now that the huge release of Steam Play Proton 7.0- 1 is out, work begins again on Proton Experimental as it pulls in all the latest changes for you to play with. What is Proton? It’s a compatibility layer designed to run Windows games from Steam on Linux. See more about it in our full guide. # ⚓ Escape_Simulator_gets_Linux_fixes,_networking_improvements –_ready_for_Steam_Deck_|_GamingOnLinux⠀⇛ A big update arrived for Escape Simulator, the online co-op puzzle game that managed to sell a lot of copies and so it should be ready for the Steam Deck. This fresh free upgrade brings in The Alchemist set to make rooms with, additional updates to the room editor with new skyboxes and particle effects, new logic items and additions to existing items to create more challenges with and code optimizations. There’s more though, they said they’ve fixed up some graphical issue for Linux and macOS, along with “Steam Deck support” – although they didn’t elaborate on what they did. Some networking improvements were also made, that the developer said “should work much better for the community rooms”. Could be a great game for the Steam Deck to run through a few puzzle rooms! # ⚓ Submerged:_Hidden_Depths_–_A_Relaxing_Experience_–_Boiling Steam⠀⇛ Submerged: Hidden Depths isn’t your typical game, where you explore, fight off enemies, then move on to the next area. The exploration is part of the game’s experience, but there’s no enemies to be had here. Please note that, even though I have access to the full game, I was asked by the publisher to only talk about what goes on during the first hour of gameplay, so as not to spoil the story for potential buyers. Submerged: Hidden Depths is the sequel to Submerged, released in August 2015. Originally a Stadia exclusive, the game will be available on Steam March 10th. You’re in control of a girl named Miku. Along with Miku is her younger brother Taku. Together, they explore a vast, open-world ocean on their fishing boat, where every now and again there’s a spot of land to walk on and discover. So kind of think of it like the sailing that’s done in Zelda: The Wind Waker. # ⚓ Caves_of_Qud_gets_a_big_content_upgrade,_improved_gamepad and_Steam_Deck_support⠀⇛ Here’s a game that will be thoroughly interesting to see on a Steam Deck. Caves of Qud is a fantastic science fantasy roguelike epic and the developers have been busy. In the latest update not only have they added in a ton more content like two minor late-game regions, 48 new Achievements, makeovers to multiple areas, new animations and more — they’ve also made big improvements to gamepad support. This new input system isn’t fully ready and so it needs be manually enabled in the control settings under the pre-release option, but even so testing with an Xbox pad today it feels pretty great. It’s good news for the Steam Deck too, as it’s enabled by default if it detects you playing on it and scales things up a bit to be clearer. o § Desktop Environments/WMs⠀➾ # § GNOME Desktop/GTK⠀➾ # ⚓ #31_Bit_Windy_·_This_Week_in_GNOME⠀⇛ Update on what happened across the GNOME project in the week from February 11 to February 18. o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ Easy_3.4.1_coming_soon⠀⇛ I built EasyOS 3.4.1RC and did some basic testing. Looks OK. Booted it on a PC with AMD Radeon HD 6870 video card and 1024×768 monitor — no problem. Good, the sun in the wallpaper is no longer squashed… # § SUSE/OpenSUSE⠀➾ # ⚓ AppArmor,_Flatpak,_GStreamer_update_in_Tumbleweed_– openSUSE_News⠀⇛ openSUSE’s rolling release Tumbleweed has produced five snapshots since our last review. Snapshots 20220215, 20220214, 20220213, 20220212 and 20220210 updated several tools, libraries and clients this week. The latest snapshot, 20220215, updated a couple Python Package Index and RubyGem packages. The package that generates profile reports from pandas DataFrame fixed almost a dozen regressions and reverted a performance speedup to fix a precision regression. The RubyGem package rubygem-faraday, which is an HTTP/REST Application Programming Interfaces client library, updated to a major new version from 1.3.0 to 2.1.0; the package added several new features like backport authorization process, improved documentation and added a policy on inclusive language. Data compression package lzip 1.23 reduced compression times by 5 to 12 percent depending on the file. Text editor vim 8.2.4375 fixed a few crashes and a couple of those involved FuncRef. An update of yast2- trans 84.87.20220211 added new pot files for storage, dns-server, nfs and s390. Snapshot 20220214 updated six packages. Flatpak 1.12.5 now detects and removes left- over data from /var/lib/flatpak/appstream and a fix was made with a display bug in Flatpak history; it does not set up an unnecessary polkit agent for flatpak’s history. An update of gnome-maps 41.4 provided some translations and fixed build issues with Meson 0.60. The update of NetworkManager 1.34.0 had multiple additions for Meson builds requirements. The updated NetworkManager also split out NetworkManager-pppoe, which is needed to configure regular PPPoE connections; the changelog states that it’s not very common since most users have PPPoE routers for the DSL connections. Internet Relay Chat client hexchat 2.16.1 updated in snapshot 20220213 and received build fixes with OpenSSL 3. The IRC client also fixed Python scripts not being opened as UTF-8. The 4.6.1 GTK4 package has a new API for text shaping engine HarfBuzz and the toolkit also fixes support for the new high- contrast setting with Wayland. The glib2 2.70.4 version updated translations and fixed a memory leak. Another packages to update in the snapshot was yast2-installation 4.4.40, which fixed some issue running with Qt 5.15. # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2022/07⠀⇛ This week, the major news is a glibc update to version 2.35. This was surprisingly smooth (so far) compared to earlier version updates. Let’s all cross our fingers for this to stay the way it is. In total, Tumbleweed has seen 6 new snapshots during this week (0210, 0212, 0213, 0214, 0215, and 0216). # § IBM/Red Hat/Fedora⠀➾ # ⚓ Fedora_Magazine:_Upgraded_Fedora_shirts⠀⇛ # ⚓ Remi_Collet:_PHP_version_7.4.28,_8.0.16_and_8.1.3⠀⇛ RPMs of PHP version 8.1.3 are available in remi-modular repository for Fedora ≥ 34 and Enterprise Linux ≥ 8 (RHEL, Alma, CentOS, Rocky…) and in remi-php81 repository for EL 7. RPMs of PHP version 8.0.16 are available in remi-modular repository for Fedora ≥ 34 and Enterprise Linux ≥ 8 (RHEL, Alma, CentOS, Rocky…) and in remi-php80 repository for EL 7. RPMs of PHP version 7.4.28 are available in remi-modular repository for Fedora ≥ 34 and Enterprise Linux ≥ 8 (RHEL, Alma, CentOS, Rocky…) and in remi-php74 repository for EL 7. # ⚓ Friday’s_Fedora_Facts:_2022-07_–_Fedora_Community Blog⠀⇛ Here’s your weekly Fedora report. Read what happened this week and what’s coming up. Your contributions are welcome (see the end of the post)! I have weekly office hours on Wednesdays in the morning and afternoon (US/Eastern time) in #fedora-meeting-1. Drop by if you have any questions or comments about the schedule, Changes, elections, or anything else. See the upcoming meetings for more information. # ⚓ Irving_Wladawsky-Berger:_How_Does_AI_Improve_Human Decision-Making?⠀⇛ “Artificial Intelligence (AI) is the newest general-purpose technology (GPT),” wrote Sukwoong Choia, Namil Kim, Junsik Kim, and Hyo Kang in a recent paper, How Does AI Improve Human Decision-Making? Evidence from the AI-Powered Go Program. “One remarkable characteristic of AI is its ability to provide humans with high-quality predictions at relatively low cost and to automate a wide range of predictions. AI has already outperformed human professionals in many domains – including strategic gameplay, medical diagnosis, and new drug development.” “Furthermore, as a GPT, the domains where AI outperforms humans are expanding at a fast pace. The rapid development and adoption of AI thus raise an interesting yet pressing question about how AI affects human tasks in these various domains. Studies of AI and human capital, for instance, have examined the performance gap between humans and AI, highlighting AI’s potential for replacing jobs.” However, we should keep in mind that new technologies have been replacing workers and transforming economies for over two centuries. But, over time, these same technologies led to the creation of whole new industries and new jobs, increasing productivity and economic output, raising earnings, and augmenting the demand for labor. Workers can increase their productivity and performance when assisted in their jobs by AI-based tools. But beyond its assistant role, AI can play a major instructional role by training human professionals to make better decisions. Recent technology advances have significantly improved the quality and reduced the cost of AI-based predictions. # ⚓ IT_talent:_6_ways_job_expectations_have_evolved⠀⇛ Enterprise IT organizations have been shaken by some tectonic shifts over the past couple of years. Tech professionals who held tight to their seats during the early months of the pandemic are now streaming toward the exits during the Great Resignation. It’s a critical time for IT leaders to realign with their team members. Specifically, it’s more important than ever to not only understand but get ahead of what IT professionals want from their employers, bosses, and teams today. People’s job expectations have shifted significantly over the last year and IT leaders must acknowledge and meet them in order to not only retain their key players but keep them engaged and happy in their roles. # § Canonical/Ubuntu Family⠀➾ # ⚓ Ubuntu_Touch_OTA-22_lands_with_video_calling improvements_and_FM_radio_daemon⠀⇛ The UBports Foundation has announced the availability of Ubuntu Touch OTA-22. It comes with plenty of improvements but among the headlines is that video calling now works in the browser (but not apps just yet) and that an FM radio daemon has been added and that the app should be available in the next release. For those already running Ubuntu Touch on one of their devices, the update can be obtained through the Updates screen of the System Settings. UBports is randomly rolling out the update to devices from today but it won’t push it out to everyone just yet in case the distribution needs to be paused to fix a major issue. If you don’t run Ubuntu Touch yet but have a device lying around that you’d like to try it on, just head over to the Ubuntu Touch devices page for instructions. # ⚓ Multiple_vulnerabilities_put_40_million_Ubuntu_users at_risk_|_TechRadar [Ed: Shoddy media pretending Snap is part of "Linux"]⠀⇛ Security researchers have recently found “multiple vulnerabilities” on Ubuntu systems, some of which would allow a threat actor to gain root privileges on the target endpoint. # ⚓ Dangerous_privilege_escalation_bugs_found_in_Linux package_manager_Snap_|_CSO_Online⠀⇛ Researchers found an easy-to-exploit vulnerability in Snap, a universal application packaging and distribution system developed for Ubuntu but available on multiple Linux distributions. The flaw allows a low-privileged user to execute malicious code as root, the highest administrative account on Linux. # ⚓ New_Linux_Privilege_Escalation_Flaw_Uncovered_in_Snap Package_Manager⠀⇛ Multiple security vulnerabilities have been disclosed in Canonical’s Snap software packaging and deployment system, the most critical of which can be exploited to escalate privilege to gain root privileges. Snaps are self-contained application packages that are designed to work on operating systems that use the Linux kernel and can be installed using a tool called snapd. o § Devices/Embedded⠀➾ # ⚓ Solderable_OSM_module_taps_i.MX8M_Mini⠀⇛ Kontron unveiled a 30 x 30mm “OSM-S i.MX8M Mini” OSM module with up to 4GB LPDDR4, which is available with a baseboard and a Linux BSP as the “BL i.MX8M Mini OSM” SBC. Iesy is prepping its own i.MX8M Mini and Rockchip PX30 based OSM modules. The Open Standard Module (OSM) form factor was developed by Kontron, F&S Elektronik Systeme, and Iesy in early 2020 when it was unveiled on F&S’ OSM-MX8MM module. Kontron has now followed up with an OSM-S i.MX8M Mini, which similarly combines a 30 x 30mm OSM Size-S form factor with an i.MX8M Mini. There is no product page so far, but the datasheet for an OSM-S i.MX8M Mini based BL i.MX8M Mini OSM SBC covers the basics. # § Open Hardware/Modding⠀➾ # ⚓ Weekly_Update_(7/2022):_Call_and_chat_with +015550199999_or_put_Ubuntu_Touch_OTA_22_on_your libhybris_phone!⠀⇛ A rather boring week: People love handhelds with keyboards, an unofficial PinePhone battery case, a translucent backcover and a little bit of software news. Oh, and PINE64 shared another community update! # ⚓ Unique_Clock_Is_All_Hands,_No_Dial,_And_Does_The_Worm |_Hackaday⠀⇛ Back in the old days, we didn’t have fancy digital clocks. No, we had good analog clocks with a big hand and a little hand, and if you wanted to know the time you had to look at the clock and figure out which number each hand was pointing at, or kind of pointing at. It wasn’t easy, and we liked it that way. So now, along comes an analog clock that’s nothing but the hands — no dial, no numbers, just hands. How is such a thing possible? The clue is in the clock’s name: AKUROBATTO, and in the video below, which shows the acrobatic movements of the clock’s hands as it does its thing. Serial improbable-clock maker [ekaggrat singh kalsi] clearly put a lot of thought into this mechanism, which consists of the hands and a separate base. The hands are joined together at one end and powered by small stepper motors. The base has two docking areas, where servo-driven claws can grasp the hand assembly, either at the center pivot or at the tip of either hand. With a little bit of shuffling around at transition points, the hands sweep out the hours and minutes in a surprisingly readable way. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ How_to_block_a_number_on_your_Android_Phone_–_Geeky Gadgets⠀⇛ # ⚓ 5_easy_ways_to_make_Android_more_ergonomic_| Computerworld⠀⇛ # ⚓ Motorola_Moto_G22_Android_smartphone_leaked_–_Geeky Gadgets⠀⇛ # ⚓ 5_Simple_Ways_to_Take_Notes_on_Android_While_You’re Offline⠀⇛ # ⚓ Samsung_Galaxy_S22_Plus_Review:_the_Best_Android Phone_You_Can_Buy⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ GTK4:_Using_GtkMediaStream_in_LibreOffice⠀⇛ Today’s GTK4 version of LibreOffice (towards 7.4) using the first cut of my efforts to use GtkMediaStream + GtkPicture for video playback. Works a lot better than this video of a video suggests 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇;-)⦈ # § Programming/Development⠀➾ # ⚓ Ruby_3.1.1_Released⠀⇛ Ruby 3.1.1 has been released. This is the first TEENY version release of the stable 3.1 series. # § Shell/Bash/Zsh/Ksh⠀➾ # ⚓ 7_Must-Know_Linux_File_Manipulation_Commands [Ed: Those are not Linux commands, they’re_mostly GNU_programs]⠀⇛ Modern Linux desktops have come a long way in regards to letting you manipulate files on your system. However, because of all the overhead resources used by a GUI (such as GNOME or KDE Plasma), when you need to work with more than one file or directory, the command line is often the fastest and most efficient way to get things done. Learning how and when to take advantage of the Linux command line with just a handful of essential file-manipulation commands will help to enhance your productivity and transform your Linux experience. # § Rust⠀➾ # ⚓ Lang_team_February_update⠀⇛ Two weeks ago, the lang team held its February planning meeting (minutes). We hold these meetings on the first Wednesday of every month. * § Leftovers⠀➾ o § Science⠀➾ # ⚓ Hello_(Many_Quantum)_World(s)_|_Hackaday⠀⇛ Historically, the first program you write for a new computer language is “Hello World,” or, if you are in Texas, “Howdy World.” But with quantum computing on the horizon, you need something better. Like “Hello Many Worlds.” [IonQ] proposes what that looks like and then writes it in seven different quantum languages in a post you should check out. # ⚓ Infinity_Mirror_Hypercrystal_Is_As_Beautiful_As_It_Sounds_| Hackaday⠀⇛ Sometimes, we feature projects that are full to the brim with advanced functionality or solve some tricky little problem for the end-user. Other times, we feature stuff that just looks super damn cool, and the Infinity Mirror Hypercrystal is firmly in that latter category. [...] The result is an infinity mirror piece that looks more advanced, more alien, and more luridly enticing than most we’ve ever seen. The dichroic shift placed on the LEDs goes a long way to elevating this sculpture to new aesthetic heights. Video after the break. # ⚓ blog.harterrt.com_–_Data_Intuition_Case_Study:_Grain-free Dog_Food⠀⇛ My vet told me I should stop feeding my dog grain- free dog food. Apparently, grain-free dog food is linked with a heart condition called Dilated Cardiomyopathy (DCM). This set off my bullshit detector, so I decided to dig deeper. [...] I have a different hypothesis for what’s going on here. I suspect this link between grain-free dog food and DCM is entirely caused by a good old- fashioned sampling bias. o § Hardware⠀➾ # ⚓ Commodore_64_Monitor_Traces_I/O_Calls,_Eases_Debugging_| Hackaday⠀⇛ Developing for the Commodore 64 can be a rewarding retrocomputing experience, and thanks to [Dave Van Wagner], things are easier with his C64 IO_Monitor project, which opens the door to logging and tracing Kernal I/O calls for closer inspection. That’s not a typo, by the way. Kernal is what handles the C64’s low-level OS routines. Amusingly, as the story goes, it did in fact originate as a misspelling of kernel, but the name stuck. # ⚓ Building_A_High-Capacity_Linear_Servo_Actuator_|_Hackaday⠀⇛ Linear actuators are useful things, moving things in straight lines rather than annoying circles like so many motors. [Retsetman] recently built a linear servo actuator of his own design with accurate positional control. The design relies on a carriage that moves along a threaded rod, perhaps the most rudimentary design of linear actuator. A large brushed DC motor is used to turn the threaded rod through a 3D-printed 9:1 herringbone geartrain, shifting the actuator back and forth. End stop switches are used to disengage the motor to avoid damage to the mechanism. Feedback is via a ten-turn potentiometer driven off the output geartrain to match the range of the actuator to the rotational range of the pot. # ⚓ VIA_SOM-9X35_Starter_Kit_features_MediaTek_i350_Arm processor_for_edge_AI_devices_–_CNX_Software⠀⇛ VIA has just introduced the SOM-9X35 Starter Kit based on MediaTek i350 quad-core Cortex-A53 processor with AI accelerator and HiFi4 DSP designed for Edge AI devices in the retail, commercial, and industrial sectors. The kit is comprised of the SOM-9X35 module with MediaTek i350 SoC, up to 4GB RAM, 16GB eMMC flash, and WiFI 5 + Bluetooth 5.0 wireless module, as well as the VIA VAB-935 3.5-inch carrier board, a 7-inch 1024×600 touch panel display, a 13MP camera module, two speakers and microphone, and accompanying accessories. # ⚓ Early_Hard_Drives:_Really_Big,_Really_Expensive⠀⇛ Today in Tedium: Hard drives may be the most fundamental building block of the computer revolution. Hitting the perfect balance between size and cost, it was a defining piece of computer history, one that made our machines more permanent and helped us rethink the way we store information. With a hard drive, we were eventually able to move away from the idea of thinking of our documents in terms of a linear order and a physical space. And that, of the many innovations that came from computing, might be the most important. Now, granted, it wasn’t easy to get to that point—in part because hard drives weren’t always the small, compact platters we have today. In fact, they were bigger. A lot bigger. Today’s Tedium talks early hard drives. [...] If you were to explain to the public what a hard drive was with no prior frame of reference, where would you start? How would you highlight the benefits to the world? That’s an odd, somewhat theoretical problem today, but in 1956, it was legitimately a challenging problem that IBM had to solve. At the time, “business machines” often meant storing information on punch cards and and typewritten pages, which meant that the file cabinet business was doing quite well back in the day. The difference between a punch card and a hard drive is quite similar to the difference between the Dewey Decimal System and microfilm—one organizes content that’s completely physical while the other shrinks the scale enough that it allows for some degree of rethinking how we access the content. With a hard disk, it doesn’t have to necessarily be in order anymore. It adds a layer of separation between you and the information being displayed. In many ways, the IBM 305 RAMAC (Random Access Method of Accounting and Control), which was initially built for the needs of accountants, represented this sort of abstraction. Designed at the behest of the U.S. Air Force, it was meant to provide faster, more efficient storage of information than magnetic drums. “This has been a day of solid achievement,” the first message ever stored on a hard drive stated, according to a 2002 ComputerWorld article. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ New_Malware_Found_Infecting_Microsoft_Teams_Meetings [Ed: Microsoft Teams itself is technically malware]⠀⇛ You may want to think twice the next time you’re on a conference call. It’s not really a time you can let your guard down. Even when doing something as innocuous as joining a chat with co-workers, you can still get hit with malware. Security experts discovered hackers have been targeting Microsoft Teams meetings with malware. # § Security⠀➾ # ⚓ Security_updates_for_Friday_[LWN.net]⠀⇛ Security updates have been issued by Debian (chromium and zsh), Fedora (microcode_ctl and zziplib), Mageia (docker-containerd, mariadb, nas, phoronix-test-suite, rlwrap, thunderbird, webkit2, wireshark, zsh, and zxing-cpp), openSUSE (aide, chromium, clamav, expat, htmldoc, libmspack, libsndfile, python-Twisted, qemu, rust, strongswan, tiff, virglrenderer, and xerces-j2), Slackware (mozilla and php), SUSE (aide, clamav, cobbler, expat, kernel, libmspack, libsndfile, python-numpy, python-Twisted, qemu, rust, strongswan, tcpdump, tiff, ucode-intel, virglrenderer, wpa_supplicant, and xerces-j2), and Ubuntu (kernel, libarchive, linux-hwe-5.13, and snapd). # ⚓ This_Week_in_Security:_Chrome_0-day,Cassandra, and_a_Cisco_PoC⠀⇛ Running Chrome or a Bhromium-based browser? Check for version 98.0.4758.102, and update if you’re not running that release or better. Quick tip, use chrome://restart to trigger an immediate restart of Chrome, just like the one that comes after an update. This is super useful especially after installing an update on Linux, using apt, dnf, or the like. CVE-2022-0609 is the big vulnerability just patched, and Google has acknowledged that it’s being exploited in the wild. It’s a use-after-free bug, meaning that the application marks a section of memory as returned to the OS, but then accesses that now-invalid memory address. The time gap between freeing and erroneously re-using the memory allows malicious code to claim that memory as its own, and write something unexpected. Google has learned their lesson about making too many details public too early, and this CVE and associated bug aren’t easily found in in the Chromium project’s source, and there doesn’t seem to be an exploit published in the Chromium code testing suite. # ⚓ Launchpad_now_supports_SSH_Ed25519_keys_and_RSA SHA-2 signatures_|_Colin_Watson’s_blog⠀⇛ As of 2022-02-16, Launchpad supports a couple of features on its SSH endpoints (git.launchpad.net, bazaar.launchpad.net, ppa.launchpad.net, and upload.ubuntu.com) that it previously didn’t: Ed25519 public keys (a well- regarded format, supported by OpenSSH since 6.5 in 2014) and signatures with existing RSA public keys using SHA- 2 rather than SHA-1 (supported by OpenSSH since 7.2 in 2016). I’m hesitant to call these features “new”, since they’ve been around for a long time elsewhere, and people might quite reasonably ask why it’s taken us so long. The problem has always been that Launchpad can’t really use a normal SSH server such as OpenSSH because it needs features that aren’t practical to implement that way, such as virtual filesystems and dynamic user key authorization against the Launchpad database. Instead, we use Twisted Conch, which is a very extensible Python SSH implementation that has generally served us well. The downside is that, because it’s an independent implementation and one that occupies a relatively small niche, it often lags behind in terms of newer protocol features. # ⚓ CISA_Compiles_Free_Cybersecurity_Services_and Tools_for_Network_Defenders_|_CISA⠀⇛ CISA has compiled and published a list of free cybersecurity services and tools to help organizations reduce cybersecurity risk and strengthen resiliency. This non-exhaustive living repository includes services provided by CISA, widely used open source tools, and free tools and services offered by private and public sector organizations across the cybersecurity community. Before turning to the free offerings, CISA strongly recommends organizations take certain foundational measures to implement a strong cybersecurity program…. # ⚓ Linux_developers_patch_security_holes_faster than_anyone_else,_says_Google_Project_Zero⠀⇛ There’s a lot of FUD about how Linux is being shown recently to be less secure than proprietary systems. That’s nonsense. But, now there are hard facts from Google’s Project Zero, Google’s security research team, showing Linux’s developers do a faster job of fixing security bugs than anyone else, including Google. # § Privacy/Surveillance⠀➾ # ⚓ Can_Pegasus_be_stopped?_|_Inside_Story_– Invidious⠀⇛ The balance between privacy and security is back in the spotlight in Europe. This time its Data Protection watchdog is sounding the alarm about the threat posed by surveillance software. Specifically, the Israeli Pegasus spyware – which could allow governments access to people’s personal information and decrypt private communications at will. # ⚓ Digital_borders:_EU_increases_use_of technology_to_monitor_migration_– InfoMigrants⠀⇛ The European Union and its border agency Frontex are using increasing amounts of technology to monitor migration at external and internal borders across Europe. Experts say that tracking technology is often being deployed to evade legal responsibilities. In February, the French government announced it would be installing additional cameras along the Channel coast to help monitor migrants hoping to cross the stretch of water towards the UK. The cameras are paid for by the British government. In December 2021, the Italian navy delivered a fresh consignment of containers with monitoring equipment to Libya to monitor migration across the Mediterranean. That’s according to research published by the investigative magazine Altreconomia (February issue). “Camera traps” like speed- monitoring devices for cars and people have also been placed on or near the border between Italy and Slovenia along the so-called Balkan route, reported the magazine. o § Environment⠀➾ # § Wildlife/Nature⠀➾ # ⚓ South_America_squid_left_exposed_amid_surge_in_China fishing⠀⇛ Negotiators from the U.S., China and 13 other governments failed to take action to protect threatened squid stocks on the high seas off South America amid a recent surge in activity by China’s distant water fishing fleet. The South Pacific Regional Fisheries Management Organization, or SPRFMO, is charged with ensuring the conservation and sustainable fishing off the west coast of South America. At the SPRFMO’s annual meeting that ended Friday, Ecuador and the European Union proposed measures that would require all ships to have observers on board by 2028 and mandate they unload their catches only in ports instead of at sea to giant refrigerated vessels — both considered key tools in limiting illegal, unreported and unregulated fishing. [...] Biologists warn that the boom has left the naturally bountiful Humboldt squid — named for the nutrient-rich current found off the west coast of South America — vulnerable to overfishing, as has occurred in Argentina, Mexico, Japan and other places where squid stocks have disappeared in the past. An investigation by The Associated Press and Spanish-language broadcaster Univision last year revealed how the traditionally lawless area has become a magnet for some of the seafood industry’s worst offenders, many of them Chinese-flagged vessels with a history of labor abuse accusations and convictions for illegal fishing. o § Civil Rights/Policing⠀➾ # ⚓ Amazon_Co-Owns_Airline_Accused_of_Operating_Torturous Deportation_Flights⠀⇛ Activists are pressuring Amazon to divest from Omni Air International, a company at the center of ICE’s deportation machine. # ⚓ PEARL_2_PEGASUS:_Bahraini_activists_hacked_with_Pegasus just_days_after_a_report_confirming_other_victims_–_The Citizen_Lab⠀⇛ Mohammed Al-Tajer is a lawyer known for being outspoken about human rights violations in Bahrain, and for defending political prisoners and activists. Al-Tajer was the president of the Bahrain Human Rights Observatory, a human rights coalition inside Bahrain. Al-Tajer was targeted with FinFisher spyware in 2011 when he received a CD containing a video of himself and his wife recorded from a hidden camera in his beach house. His computer was infected with FinFisher around the same time he received the CD. Al-Tajer’s wife, Dr. Huda, was detained for her activism during the 2011 uprising for providing medical aid to injured protesters. Ultimately, Al- Tajer did not accede to the blackmail demands, and the video was circulated online on pro-government forums and social media accounts. [...] In March 2019, Dr. Siwar conducted an Instagram Live interview with a school student reportedly expelled for dealing Lyrica, a prescription anti- anxiety medication that is sometimes abused to produce a “relaxed and euphoric” high. The student said that she was part of an organized drug-dealing group in Hamad Town Intermediate Girls School. Dr. Siwar said that “powerful people” were implicated in the drug dealing. Bahrain Mirror later revealed that Dr. Siwar was referring to the King’s fifth son, Khalid bin Hamad Al Khalifa. Bahrain’s then Prime Minister announced an investigation into Dr. Siwar’s allegations. The investigative report stated that the Lyrica incident was isolated, and that Dr. Siwar was guilty of slander and defamation. Dr. Siwar was sentenced to a year’s imprisonment in the case. Dr. Siwar also faced other allegations: a pro- government newspaper announced that she would be charged with “covering up a rape,” and she was sentenced to a year in prison for reportedly providing Panadol (a medicine similar to Tylenol) to a mentally ill teenager. Although Dr. Siwar was pardoned by Bahrain’s King in May 2021 after spending several months in prison, the prosecution re-introduced the same case in court again in November 2021. When she was summoned in the case, she fled to the UK and sought asylum. Further, in January 2022, the Ministry of Interior’s General Directorate of Anti-Corruption and Economic & Electronic Security began legal action against Dr. Siwar after several individuals complained that Dr. Siwar’s Instagram video had defamed them. The Directorate also accused Dr. Siwar of practicing medicine without a license, defaming employees of a ministry and spreading false information during her court hearing. # ⚓ Civil_society_calls_for_solidarity_with_Ukraine’s_human rights_defenders_in_guarding_against_cyber_threats⠀⇛ In a statement issued today, Access Now, together with Centre for Democracy and Rule of Law and Digital Security Lab Ukraine, calls on the international community to take swift action in support of civil society in Ukraine, as well as the broader public whose human rights are being undermined by cyberattacks on Ukraine’s critical infrastructure. Following the most recent cyberattacks on January 13-14 and February 15, 2022 targeting Ukraine’s essential public service infrastructure, and the ongoing threat of escalating Russian aggression, this is a critical moment for solidarity with Ukrainian civil society. [...] “Cyberattacks are disrupting the ability of Ukrainians to seek medical care and obtain other essential services, and receive important information amidst the intensifying military conflict. The international community must act now to protect Ukraine’s critical infrastructure and human rights defenders from these attacks,” said Anastasiya Zhyrmont, Regional Outreach Coordinator for Eastern Europe & Central Asia at Access Now. # ⚓ [Attacks]_on_Ukraine’s_infrastructure_and_civil_society violate_human_rights⠀⇛ There is a pressing need to provide Ukrainian civil society with technical means to protect both themselves and the sensitive data on their servers and devices, as well as to prevent future attacks. We urge tech companies, nonprofits, and funders to expand their support programs and provide Ukrainian activists with free and secure VPNs, antivirus programs, encryption, DDoS protection, and other essential digital tools, equipment, and services. o § Internet Policy/Net Neutrality⠀➾ # ⚓ #SocialMediaComplianceWatch:_analysis_of_Social_Media Compliance_Reports_for_the_month_of_December_2021⠀⇛ Google (including YouTube), Facebook, Instagram (both are now under Meta), ShareChat, Snap, Twitter and WhatsApp have released their reports in compliance with Rule 4(1)(d) of the IT Rules 2021 for the month of December, 2021. The latest of these was published by Meta and was made available in late January 2022. The reports contain similar shortcomings, which exhibit lack of effort on the part of the social media intermediaries and the government to further transparency and accountability in platform governance. The intermediaries have yet again, not reported on government requests, used misleading metrics, and also have not disclosed how they use algorithms for proactive monitoring. You can read our analysis of the previous reports here. o § Digital Restrictions (DRM)⠀➾ # ⚓ Bionic_Eyes_Go_Dark⠀⇛ If you were blind, having an artificial retinal implant would mean the difference between seeing a few hundred pixels in greyscale and seeing all black, all the time. Imagine that you emerged from this total darkness, enjoyed a few years of mobility and your newfound sense, and then everything goes dark again because the company making the devices abandoned them for financial reasons. This is a harrowing tale of close-source technology, and how a medical device that relies on proprietary hard- and software essentially holds its users hostage to the financial well-being of the company that produces it. When that company is a brash startup, with plans of making money by eventually pivoting away from retinal implants to direct cortical stimulation — a technology that’s in it’s infancy at best right now — that’s a risky bet to take. But these were people with no other alternative, and the technology is, or was, amazing. [...] If we were CEO of SecondSight, we know what we would do with our closed-source software and hardware right now. The company is facing bankruptcy, has lost significant credibility in the medical devices industry, and is looking to pivot away from the Argus system anyway. They have little to lose, and a tremendous amount of goodwill to gain, by enabling people to fix their own eyes. # ⚓ Why_is_John_Deere_so_opposed_to_letting_farmers_fix_their stuff?_—_The_Repair_Association⠀⇛ John Deere is trying to block the agricultural Right to Repair in Nebraska—which affects all of us, not just farmers. When farm equipment goes down in the middle of the season, it can cost farmers a harvest and the rest of us a meal. Everyone that eats has a horse in this race. And Deere is rigging the race. They have filled Nebraska’s unicameral legislature with their lobbyists attempting to block the passage of LB543, the Right to Repair for Agricultural and Ranch Equipment. They are telling senators that Deere & Co. supports farmers repairing their equipment, but they don’t support the “right to modify” When pressed, they proclaim that farmers can already fix 98% of their equipment, so there isn’t a problem for legislators to address. Hogwash. Within the 2% of repairs that Deere blocks are many problems that can take a machine down 100%. Fixing 98% of something rather than 100% is a farce. Limp mode can be a death sentence for a crop. when a simple problem during key times takes the machine down 100%, not 98%. Plus, repair is not modification. Most farmers have no interest in doing anything with their tractor beyond the job it was designed to do—they just want it to be in good working order. So why is Deere paying lobbyists big bucks to bend the ears of every Nebraskan senator, to keep farmers away from 2% of repairs? Why are they fighting 5 antitrust lawsuits already so far this month? What is Deere protecting so fiercely? < ䷩ 𝚕𝚒𝚗𝚎 8024 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.18.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_18/2/2022:_Bottles_2022.2.14_and_RedNotebook_2.23⠀✐ Posted in News_Roundup at 11:55 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Chrome_OS_Flex_can_be_installed_on_EOL_Chromebooks,_but Google_doesn’t_recommend_it⠀⇛ # ⚓ Lilbits:_Windows_11_Pro_will_require_Microsoft_accounts, using_Chrome_OS_Flex_to_keep_old_Chromebooks_alive_– Liliputing⠀⇛ That could come in handy if you have an older model that’s no longer covered by Google’s Auto Update policy, which means that it’s no longer receiving new builds of Chrome OS with new features or security updates. Chrome OS Flex could provide a way to run an up-to-date build of Chrome OS on old gear… but it’s not without its own risks. Google officially advises against using Chrome OS Flex on Chromebooks that have passed their Auto Update Expiration dates, noting that Google doesn’t officially support this use case and that users may run into issues with the installation process, may have firmware or other hardware compatibility problems, and may not receive updates. That said, a number of users have already reported success installing Chrome OS Flex on older Chromebooks, which, quite honestly is probably better than running a 2-year-old version of Chrome OS without the latest security patches, even if those devices never receive another update. o § Audiocasts/Shows⠀➾ # ⚓ Technically_Speaking_(E11):_You_need_Ops_to_AIOps_– Invidious [Ed: Red Hat slinging buzzwords, as usual]⠀⇛ o § Kernel Space⠀➾ # ⚓ Btrfs_Vs._Ext4:_Essentials,_Benefits,_And_Disadvantages⠀⇛ File systems control where and how your data is stored and retrieved from a storage device. Windows and macOS users have little reason to worry about file systems since NTFS and HFS+ are the only choice of filesystems they have, respectively. Linux users have the flexibility to choose the file system their machine uses since the kernel supports a variety of these. Ext4 is the default option for Linux users. Still, there is another file system called Btrfs you could consider using. With a part of the Linux community pushing for the adoption of Btrfs as the default file system, it’s essential to understand the functionalities, advantages, and disadvantages of both. # ⚓ RAID_expansion_comes_to_OpenZFS_at_last⠀⇛ ZFS has been around for 16 years and has a solid reputation, but it does have limitations compared to its rivals. One of these is in the process of being lifted: soon it will be possible to add space to an existing ZFS array. As long as you’re using FreeBSD, anyway. Filesystems are one of the core differentiators between enterprise Linux distributions (and other Unix and Unix-like OSes). That means, like anything in the Unix world, there’s “advocacy” – in other words, bitter squabbling about which is best or worst. ZFS was originally developed by Sun for Solaris. At one point, Apple was going to adopt it, but changed its mind. Now, of course, Oracle owns it – but there is OpenZFS, and a very small chance that the situation might change. o § Applications⠀➾ # ⚓ Review:_Harmonoid_–_music_app⠀⇛ We’ve reviewed a whole raft of open source music players from tiny command-line players to bloated Electron-based heavyweights. But Linux is endowed with a huge selection, and there’s still a few we’ve yet to put under the microscope. Harmonoid is billed as an elegant music app to play local music and YouTube music. It’s written in the Dart programming language and published under an open source license. Before we see how it fares, let’s briefly cover the installation process. # ⚓ Okular:_Signature_verification_User_Interface_added_to Okular_mobile_interface⠀⇛ Okular has two user interfaces, you can control which one you get when compiling okular by setting the OKULAR_UI cmake variable to desktop (the default) or to mobile (which you can build just fine on the desktop too, there’s nothing “mobile only” in it). The mobile one is built on top of Kirigami and is more oriented to use with touch screens. It also has fewer features, for example, you can’t add annotations nor fill forms. I could say it’s less likely you need those features on a mobile form factor but that’s less and less true as time goes and computing shifts to mobile devices, but that’s a story for another day. # ⚓ What_is_XRDP?_|_ITProPortal⠀⇛ XRDP is one of the best remote desktop software tools for operating systems other than Windows, such as Linux. # ⚓ RedNotebook_2.23⠀⇛ RedNotebook is a modern desktop journal. It lets you format, tag and search your entries. You can also add pictures, links and customizable templates, spell check your notes, and export to plain text, HTML, Latex or PDF. RedNotebook is Free Software under the GPL. o § Instructionals/Technical⠀➾ # ⚓ Comparing_lzop_and_plzip_compression⠀⇛ I had a fascination with file compression in the 2000s, but OpenZFS’s inline compression has spoiled me ever since. When I need to leave its comforting confides though, I turn to the excellent lzop and plzip tools, which have largely replaced gzip and bzip2 for my one off archives. # ⚓ What_Is_AAA_Security?⠀⇛ Authentication, authorization, and accounting, often called AAA or Triple-A, are sets of services and protocols that enable granular access control over computer networks. Before the popularity of mainstream HTTP-based authentication protocols such as OAuth and SAML, AAA protocols were the primary way to authenticate users or machines to network services. AAA protocols are still commonly found in corporate LAN and WAN networks, ISPs, cellular networks, and network devices such as firewalls, routers, and switches. # ⚓ Lurking_complexities_in_a_web_server_that_just_serves static_files⠀⇛ The essentially mandatory complexity is setting a good Content-Type so that browsers are willing to interpret your HTML and CSS as HTML and CSS. In a dynamic site, this is something the application handles; in a static site, you have a blob of bytes and now you get to figure it out. The traditional answer is to use file name extensions along with a small or big mapping table from extensions to Content-Type, but you’re responsible for that code and that table (either hard-coded or with a way to configure it at runtime and an initial default version). # ⚓ Testing_Raspberry_Pi’s_new_Network_Install_feature⠀⇛ Like Apple’s Internet Recovery, you don’t have to have any OS installed on your computer to use it. And you don’t need to run a separate server to boot your Pi and image its drive. (Note: There are also some PC vendors who have specific image-over- Internet services for certain devices like the Microsoft Surface, but they’re not universally applicable to all PC builds.) This feature is NOT netbooting. The Pi supports that too. This is similar, in a sense, but this goes deeper. # ⚓ How_to_install_and_Use_Tripwire_on_Debian_11⠀⇛ Hello, friends. In this post, you will learn how to install and use Tripwire on Debian 11. This intrusion detection system is a vital tool for many sysadmins. [...] Tripwire is an intrusion detection system that will help us to further improve server security. To accomplish this, Tripwire is constantly updating critical system files. In addition to this, it also reports control reports in case they have been modified or deleted by a hacker. In short, it scans sensitive files for changes. Fortunately, Tripwire is an open-source tool with outstanding Linux support. This means that the installation process will be easy to do. Let’s go for it. # ⚓ Ceph_Storage_5:_Insert_next_disk⠀⇛ Red Hat Ceph Storage 5 introduces cephadm, a new integrated control plane that is part of the storage system itself, and enjoys a complete understanding of the cluster’s current state — something that external tools could not quite achieve as well because of their external nature. Among its many advantages, cephadm unified control of the state of a storage cluster significantly simplifies operations. [...] A failed OSDs in a Ceph Storage cluster can also be replaced by a junior administrator with appropriate role-based access control (RBAC) permissions on the Dashboard. OSD IDs can be preserved while replacing the failed OSDs, which is both operationally easier to manage (by having a fixed set of ID assigned to each host) and optimizes memory usage (OSD ID gaps are undesirable). The Cluster administrator can thus use the Dashboard’s RBAC capabilities to delegate a trainee to replace failed drives, without delegating additional permissions that the junior administrator is not yet qualified to operate, as detailed in the following short video. # ⚓ How_to_Install_and_Use_ZSH_Shell_in_Linux⠀⇛ A shell is used as an interface between a user and the operating system. On most Linux distributions, bash shell is the default shell used, however, the best part about open source is choice. As users, we can decide to change defaults that came with the system and use other alternatives. In Linux, the most commonly used open-source shells include Bourne Again Shell (bash), tcsh (an enhanced C shell), Korn shell (ksh), friendly interactive shell (fish), and zsh. # ⚓ How_to_Install_Budgie_Desktop_on_AlmaLinux_|_Rocky_Linux_8 –_Linux_Shout⠀⇛ Learn the steps to install the Budgie Desktop environment on Almalinux 8 and Rocky Linux 8 using the command terminal. One of the greatest benefits of using Linux OS is we can use multiple Desktop User Interface of choice. This allows users to modify and get the Desktop Interface of their own choice. Well, Gnome is the popular one that comes as a default GUI in both AlmaLinux and Rocky. However, it is not suitable for everyone. Few users want a lightweight but with nice, sleek, and familiar looks. If you are one of the then try the Budgie Desktop environment. Budgie comes as a default GUI in Solus operating systems, an independent Linux. And Budgie is a part of this project. However, as it is published under an open-source license we can install it on any popular Linux either by adding some third-party repository or the system’s base repo. o § Wine or Emulation⠀➾ # ⚓ Bottles_2022.2.14_Release_Lets_You_Easily_Install_Windows Apps_on_Linux_–_It’s_FOSS_News⠀⇛ You can use Wine to install Windows apps on Linux, but it does not work for all the applications. Moreover, it requires you to configure things manually. So, what are the easy options? While CrossOver has been trying its best to make the process easier, Bottles is another solution. With Bottles’ latest release, it aims to make things seamless to help run your preferred Windows app with minimal tweaking. o § Games⠀➾ # ⚓ Valve_remedies_shader_caching_issues_with_Proton_games before_Steam_Deck_launch⠀⇛ Shader caching exists to reduce the amount of work your GPU needs to do when running a game. But Proton users have had issues with the way Steam caches them for some time now. Thankfully, the latest Steam beta release from Valve seeks to solve some of these issues, and just in time for when the Proton-dependent Steam Deck begins shipping later this month. [...] Right now, this is just in the beta release of Steam. But by the time later pre-orders of the Deck begin hitting doorsteps, it will likely be moved into the main release. In the meantime, those who have been suffering from shader cache-related issues can opt in to the beta version of Steam within the settings of the Steam client. Once that’s done, Steam should automatically update itself to the latest beta release, complete with all related features. # ⚓ An_interview_with_James_Spanos_of_Wormwood_Studios_| GamingOnLinux⠀⇛ You asked: we delivered. Here’s a chat with game developer extraordinaire James Spanos, who works with Wormwood Studios and publisher Wadjet Eye Games. Q: Could you first introduce yourself and tell us about your games? “My name is James Spanos, I’m a game developer, with the major role of coder for Wormwood Studios, and working for/with Wadjet Eye Games, our publisher. I’ve worked on Primordia and Strangeland, both point and click adventure games released in 2012 and 2021, under Wormwood Studios, but I’ve worked on various titles throughout the years, like The Cat Lady and Downfall by Harvester Games, where I did some interface work for, and Mage’s Initiation, where I worked on the combat system! I’ve been a gamer my whole life, so being able to work full time as a gamedev was always something I aspired to!” # ⚓ 1_week_from_release,_Steam_Deck_hits_well_over_640_Playable games_|_GamingOnLinux⠀⇛ We’re now only a single week away from something amazing, Valve will be officially releasing the Steam Deck. Here’s some updated numbers on what games you can expect to see working well. Looking back, 6 days ago we noted there we 520 games rated as Verified or Playable together and the list has just kept growing. # ⚓ Devolver_Digital_announces_save-the-day_adventure_McPixel_3 |_GamingOnLinux⠀⇛ McPixel 3 is coming from Sos Sosowski and Devolver Digital – but what happened to number 2? Guess that one got lost adventuring. Even their official announcement email was confused, telling us to join them in asking “What the hell happened to McPixel 2?”. The original released back in 2012 and this follow- up is described as: “Is it a bird? Is it a plane? It’s falling too fast to be either of those. It’s McPixel! A wanna-be hero who keeps getting mixed up in the most unbelievable situations you can imagine. Avert one disaster after another at every turn using unconventional yet entertaining methods of mayhem including – but not limited to – summoning a spider-billionaire, having a BBQ in his pants, punching a T-Rex into outer space, peeing into sports cars, and kicking Fork Parker in the balls.” # ⚓ itch.io_has_another_Creator_Day_today,_100%_goes_to developers_|_GamingOnLinux⠀⇛ Game store itch.io, well known for helping out indies and running Game Jams has today put up another Creator Day. For 24 hours, until midnight Pacific Time (8AM Saturday UTC), itch will give 100% of the revenue to creators (minus taxes and normal fees). It’s a really good way to support some smaller developers! o § Distributions⠀➾ # ⚓ 2021_hardcore_list_of_linux_distributions_without_elogind and_other_systemd_parts⠀⇛ This list is going to be short and there may be a sublist of distros with a medium strict standard. We shall explain what the object is, below the short list (which we hope the community will assist in making longer as we have not been able to currently review the work of every distro and fork). # § BSD⠀➾ # ⚓ Debugging_an_ioctl_Problem_on_OpenBSD⠀⇛ I was trying to use a V4L2 Ruby module on my OpenBSD laptop but ran into a problem where sending the V4L2 ioctls from this module would fail, while other V4L2 programs on OpenBSD worked fine. Since I got a few questions recently about kernel development and debugging, I thought I’d write up how I finally tracked it down and fixed it. (Spoiler: it was not an OpenBSD problem.) # ⚓ My_journey_from_macOS_to_FreeBSD⠀⇛ I would like to share my personal experience with my recent move to the PC world. My journey started on MS DOS and then Windows, as it’s common for many people. Later on I moved to Linux, but only on desktop. When the time came and I needed a laptop, I was fascinated by the hardware and software quality of Macintosh. Back then, it was an era of PowerPC, that was coming slowly to an end. I bought my first MacBook Pro around 2007 and I was really satisfied with it. I loved the Unix roots of Mac OS X. It was a combination of Mach kernel and FreeBSD user land that gave it it’s unique strength and architecture. I absolutely fell in love with Aqua interface of Mac OS X Tiger. All those glossy, beautiful buttons and scrollbars really captured my heart. # § Gentoo Family⠀➾ # ⚓ Gentoo:_Format_of_download_file_signatures_has changed⠀⇛ We have simplified the format of the downloadable file (i.e. stage 3 and iso image) signatures. Now, each of these files is accompanied by a detached GnuPG signature where the file itself is signed. The signing key remains unchanged; see our web page on release media signatures for the fingerprints. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Nebulon_adds_Ansible_support_for_infrastructure deployment⠀⇛ Nebulon has integrated its smartInfrastructure platform with Red Hat’s Ansible software – including a set of modules that allow users to automate Nebulon infrastructure deployment and management by using Ansible Playbooks. The Nebulon Ansible Collection, when combined with the firm’s Nebulon ON cloud-based control plane used for management, is claimed to reduce operational overheads by up to 75 per cent compared with operating hyperconverged infrastructure (HCI) or traditional three-tier server infrastructure, according to Nebulon. Nebulon’s infrastructure platform is based on a PCIe card called the Services Processing Unit (SPU), which fits inside server nodes and controls all the storage drives in each node. Each SPU is linked to all the others in a cluster via dedicated Ethernet connections, effectively producing a kind of distributed storage area network (SAN) that is configurable via the cloud-hosted Nebulon ON control plane. # ⚓ IBM_merges_13_APAC_nations_into_one_regional organization [Ed: IBM still cooking the books to hide its constant decline]⠀⇛ IBM quietly reorganized its Asian affairs at the start of 2022, creating a region called ASEANZK that means big markets such as Australia and South Korea now report to a regional entity. ASEANZK (gesundheit) comprises the ten ASEAN member countries – Brunei, Cambodia, Indonesia, Laos, Malaysia, Myanmar, the Philippines, Singapore, Thailand, and Vietnam – plus Australia, New Zealand and South Korea. The Register understands that the ASEAN group previously operated as a region, and the three other nations stood alone. # ⚓ IBM_Consulting_assimilates_cloud_firm_for_Azure expertise [Ed: IBM is shilling Microsoft]⠀⇛ IBM has acquired Neudesic, a US cloud consultancy services firm specialising in Microsoft’s Azure platform, as part of a continued drive to expand the company’s growth in hybrid multicloud services. # ⚓ SAP_&_IBM_Join_Forces_to_Rev_Up_Workload_Transition to_Cloud [Ed: “Transition to Cloud” as in changing the word server to “CLOUD"]⠀⇛ # ⚓ IBM_Cloud_to_offer_Z-series_mainframes_for_first_time –_albeit_for_test_and_dev⠀⇛ As IBM tries to address allegations it discriminated against older staff, the IT giant has for the first time brought its oldest computing platform – the mainframe – into the age of infrastructure-as-a-service. The 111-year-old tech institution today announced it will offer the Z mainframe platform on the IBM Cloud, by offering virtual machines running z/OS as-a-service. # ⚓ IBM_HR_chief_insists_‘no_systemic_age discrimination’⠀⇛ Memo responds to lawsuit brought by wife of exec who killed himself after layoff IBM’s Chief Human Resources Officer Nickle LaMoreaux on Sunday rejected what she described as “false claims of age discrimination at the company.” “Discrimination of any kind is entirely against our culture and who we are at IBM, and there was (and is) no systemic age discrimination at our company,” said LaMoreaux in a public statement posted to the company’s website. The media reports she references follow from the release of documents in an age discrimination lawsuit against the venerable computing biz, Lohnn v. IBM. The initial complaint was filed in July 2021 [PDF] on behalf of Jorgen Lohnn, who took his own life after being laid off from the company. “Jorgen Lohnn worked for IBM for approximately 15 years until his layoff in 2016 at the age of 57,” the initial complaint says. “He worked for IBM as a Client Executive for Sales and Distribution. He committed suicide after his layoff from IBM. # ⚓ Controlling_software_supply_chain_security_will require_new_tools,_automation_and_vigilance ⠀⇛ “It’s called a supply chain, and it’s only as strong as its weakest link,” said Vincent Danen, vice president of product security at Red Hat Inc., in an interview with theCUBE, SiliconANGLE Media’s livestreaming studio. “If one company is breached, multiple companies end up being breached as a result of that. I don’t look at it as we’re just securing Red Hat. We’re securing our customers, and we’re also doing that for their customers as well.” # ⚓ Idevnews_|_API_Management_vs._Service_Mesh:_The Choice_Doesn’t_Have_to_Be_Yours⠀⇛ As organizations look to keep up with our increasingly digital and cloud-driven world, many are modernizing their IT infrastructure and adopting API-centric and microservices- based architectures to improve speed, agility, and efficiency. Such uses of APIs support the rapid-response expectation of the modern era. In this case, APIs take the weight of a monolithic application and break it down into small microservices—which become independent units that promote agility when managing and scaling applications. Consistent and effective management of these interfaces and services is critical for successful deployment and use. # § Debian Family⠀➾ # ⚓ A_twisted_maze_of_dependencies⠀⇛ My relative inexperience with Debian systems means I’m constantly being delighted to discover that such and such has already been packaged up and is just an apt command away. Things that I would have done by hand in the years up to this point now have someone else worrying about them. Unfortunately, the packagers can only work with what they’ve been given, and in the case of certain ecosystems, that means an explosion of crazy. Case in point: the other night, I was working on some Javascript code (unavoidable for the problem at hand), wanted to see how much I had screwed up, and thought “hmm, there was this jshint thing that would show me where I did something stupid back in the day”. I went looking and didn’t find that, but did find something called “eslint”. I figured, okay, es, ECMAScript, that’s the fancy name for this stuff now, should work, right? # § Canonical/Ubuntu Family⠀➾ # ⚓ Unlock_Multi-Touch_Gestures_in_Xubuntu_—_Sean_Davis⠀⇛ One of the features I’ve grown to appreciate since using macOS, elementary OS, and GNOME 4x is multi-touch gestures for switching workspaces. When I came back to Xubuntu, I ran into some roadblocks bringing my favorite feature into Xfce. By disabling the Synaptics driver and installing Touchégg, you can bring Magic Trackpad support and gestures to Xubuntu. # ⚓ Ubuntu_Touch_OTA-22_Rolling_Out_Now_with_Initial_FM Radio_Support,_WebGL_Support⠀⇛ Ubuntu Touch OTA-22 is here one and a half months after the OTA-21 update to add yet another layer of improvements, as well as to pave the way for new, upcoming features, such as FM Radio support to allow for real analog radio listening on supported devices. For now, only the daemon implementation landed in the OTA-22 release, while an FM Radio application should be available in the app store in the next few weeks. o § Devices/Embedded⠀➾ # § Open Hardware/Modding⠀➾ # ⚓ OPPO_announces_tie-up_with_Hasselblad_for_camera tech⠀⇛ Chinese phone manufacturer OPPO has announced a three-year partnership with the famous camera firm Hasselblad to develop camera technology for its flagship Find series. # ⚓ Linking_AI_education_to_meaningful_projects⠀⇛ # ⚓ How_to_update_the_Raspberry_Pi_Compute_Module_4 Bootloader_/_EEPROM⠀⇛ The Raspberry Pi 4 and Pi 400 share the same Broadcom BCM2711 SoC with the Compute Module 4. All three devices also share an SPI EEPROM flash chip, which stores the Raspberry Pi’s bootloader. But the Compute Module 4 differs in how you update the bootloader. With the Pi 4 or Pi 400, you can use Raspberry Pi imager to write a utility image to a microSD card to update the bootloader. You put in the card, power on the Pi, and the bootloader is updated. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ List_of_Xiaomi_smartphones_that_will_be_updated_to Android_13⠀⇛ # ⚓ ExpressBasics:_How_to_block_unwanted_notifications_on Android_|_Technology_News,The_Indian_Express⠀⇛ # ⚓ 5_easy_ways_to_make_Android_more_ergonomic_| Computerworld⠀⇛ # ⚓ 7_Best_Android_Email_Apps_to_Use_in_2022_–_TechPP⠀⇛ # ⚓ JingPad_A1_bootloader_unlock_tool,_Android_ROM,_and source_code_are_now_available⠀⇛ # ⚓ This_Could_Be_OPPO’s_Very_First_Android_Tablet⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # ⚓ Our_Old_Friend,_the_Data_URL⠀⇛ I first looked into data URLs seriously after encountering them in Sean Conner’s (now defunct) Gemini client torture test, shortly after I started working on Lagrange. I’ve since seen these being played with here and there. When you think about it, data URLs have untapped potential for Gemini. Due to the stipulation that each user action results in no more than a single network request, the usual way of accessing documents composed of heterogeneous content is unavailable. With data URLs, though, it is possible to embed images, CSV-tables, and whatever else into a perfectly normal, spec-compliant Gemtext file — without any ambiguity or new semantics. And the best part is that since clients normally hide raw URLs for basic readability, this doesn’t cause (well written) clients to misbehave when encountering such a URL. # ⚓ How_Everything_We’re_Told_About_Website_Identity Assurance_is_Wrong⠀⇛ This isn’t all going to be in the order in which DigiCert has presented the information, instead I’m going to walk through it in a fashion which systematically breaks it apart and shoots it down in flames. Let’s start here: [...] # ⚓ Web_Security_Basics:_XSS⠀⇛ I decided to learn more about areas of web development I don’t know a lot about. You know,…stuff like SEO and web security. I’ll share my findings here on my blog and I’ll try to do as much research as possible, but please keep in mind that I’m a noob concerning these topics. I began watching Feross Aboukhadijeh’s fantastic Web Security lecture, which inspired me to learn more about web security. This first post is about Cross Site Scripting (XSS). # § Mozilla⠀➾ # ⚓ Is_Firefox_OK?⠀⇛ At the end of 2008, Firefox was flying high. Twenty percent of the 1.5 billion people online were using Mozilla’s browser to navigate the web. In Indonesia, Macedonia, and Slovenia, more than half of everyone going online was using Firefox. “Our market share in the regions above has been growing like crazy,” Ken Kovash, Mozilla’s president at the time, wrote in a blog post. Almost 15 years later, things aren’t so rosy. Across all devices, the browser has slid to less than 4 percent of the market—on mobile it’s a measly half a percent. “Looking back five years and looking at our market share and our own numbers that we publish, there’s no denying the decline,” says Selena Deckelmann, senior vice president of Firefox. Mozilla’s own statistics show a drop of around 30 million monthly active users from the start of 2019 to the start of 2022. “In the last couple years, what we’ve seen is actually a pretty substantial flattening,” Deckelmann adds. # ⚓ The_Talospace_Project:_Firefox_97_on_POWER⠀⇛ It was previously reported that WebRTC was broken on OpenPOWER under Fx96, which looks like bug 1738445 (a replay of bug 1465274, which I upstreamed four years ago). I don’t use WebRTC myself due to the way my internal network is configured, so don’t consider this in any way an attestation of functionality, but I was able to build Firefox 97 unmodified with the .mozconfigs and LTO-PGO patch from Firefox 95. Although I have an old build of gn, I tested whether that was the necessary piece by pulling that line out of the configuration, and it still built — at least under gcc. I did do a test clang build (removing the compiler export lines and removing forcing linkage with bfd), and that did fail to build (with or without gn), and –disable-webrtc along with this change to NSS did allow it to compile. However, when started up with ./mach run, the clang build could browse but complained the history and places databases were corrupt and about: support was messed up. Using the same profile with a gcc build was fine. IDK. # § FSF⠀➾ # § Licensing/Legal⠀➾ # ⚓ Can_Open-Source_Software_enforcement_help_save the_planet?⠀⇛ The Software Freedom Conservancy (SFC) has sued smart TV manufacturer Vizio for alleged breaches of open-source software (OSS) licenses. # § Programming/Development⠀➾ # ⚓ Golang_gRPC_Example⠀⇛ Welcome back. I’m an experienced developer, learning Golang by building an activity tracker. Last time I added SQLite persistence. Today, I’m going to be porting everything to gRPC. If you’re curious about gRPC – how it works, when to use it, what example code might look like – well, you are in luck because I’m going to be building a grpc client, a grpc server, and the protobuf files for my activity tracker. The full code is on GitHub. # ⚓ Insomnia_is_an_open-source_Postman_alternative_with GraphQL_support⠀⇛ Insomnia is a free, open-source API design and test tool for individual developers and enterprises. # ⚓ Recent_updates_in_Conan_package_manager_support⠀⇛ In our previous blog post about Installing Qt via Conan Package Manager, we introduced how to use Conan package manager with Qt. Now it’s time to look at the recent enhancements in our Conan story. # § Rust⠀➾ # ⚓ Rust_Use_Continues_To_Increase⠀⇛ The 2021 Rust Survey, the results of which have just come out, show not only increased use of the language for work purposes but also that developers are gaining confidence for using it for production-ready code. * § Leftovers⠀➾ o ⚓ Mitski’s_Ghost_Stories⠀⇛ Three years ago, during the summer of 2019, Mitski announced a hiatus. For the past five years, she’d been touring nonstop. The 2016 breakout success of her fourth studio album, Puberty 2, had vaulted her from a well- loved indie artist to a crossover success story, then onward and upward into the firmament of pop stardom. Lorde tapped her as an opening act in her 2018 Melodrama tour; Iggy Pop name-checked her on his radio show; her subsequent album, 2018’s Be the Cowboy, was a perennial favorite on year-end lists. She still didn’t have a permanent mailing address and stored her things at her parents’ house, but no matter—she was, as NPR crowned her, the 21st century’s poet laureate of young adulthood, and her future, as Pitchfork declared, was “limitless.”   o ⚓ Uber_and_Lyft_are_taking_on_healthcare,_and_drivers_are_just along_for_the_ride⠀⇛ Correll is now working as a lawyer. But if he had kept driving, he might have run into more situations like this one. That’s because, for the past few years, rideshare companies Lyft and Uber have been moving into the non- emergency medical transportation (NEMT) business, offering their networks to healthcare organizations that need to schedule rides for patients. Correll isn’t sure if his ride was through a formal NEMT program, but it could have been: to protect patient privacy, drivers aren’t told if their rides are from healthcare partnerships or not. o § Education⠀➾ # ⚓ God,_Grades_and_College⠀⇛ But one often overlooked demographic factor is religion. The U.S. is the most devout wealthy Western democracy. Does a religious upbringing influence teens’ academic outcomes? Over the past 30 years, sociologists and economists have conducted several studies that consistently show a positive relationship between religiosity and academic success. These studies show that more religious students earn better grades and complete more schooling than less religious peers. But researchers debate what these findings really mean, and whether the seeming effect of religiosity on students’ performance is really about religion, or a result of other underlying factors. # ⚓ Book_Notes:_“Millions,_Billions,_Zillions”_by_Brian Kernighan⠀⇛ Just because there are numbers attached to a presentation of fact doesn’t mean it’s true. Or even based in reality. But we too easily become “number numb”: [...] o § Hardware⠀➾ # ⚓ Semiconductor_market_correction_could_come_in_2024_•_The Register⠀⇛ The semiconductor world’s continuing roaring sales growth could hit a wall in 2024, an industry research firm has predicted. IC Insights is projecting sustained semiconductor revenue growth in 2022 and 2023, with a market correction due the year after that. “2024 is currently expected to be the next cyclical downturn in the market, and 2025-2026 will return to growth years,” Brian Matas, vice president of market research, told The Register. The semiconductor sector is highly volatile, with up cycles in which chip demand outstrips the supply – as we’re seeing right now – followed by down cycles resulting in oversupply. # ⚓ HC32L110_Arm_Cortex-M0+_MCU_is_available_in_a_tiny_1.59_x 1.436_mm_CSP16_package_–_CNX_Software⠀⇛ The microcontroller seems to have been released in 2020, and there’s plenty of documentation on the product page. You’ll also find the software development tools, and IAR Embedded and Arm Keil MDK are the recommended/supported IDEs for the microcontroller. Everything is in Chinese, but this may change soon if LilyGO releases the board for the “overseas market”. # ⚓ AMD_Completes_Acquisition_of_Xilinx⠀⇛ AMD (NASDAQ: AMD) today announced the completion of its acquisition of Xilinx in an all-stock transaction. The acquisition, originally announced on October 27, 2020, creates the industry’s high- performance and adaptive computing leader with significantly expanded scale and the strongest portfolio of leadership computing, graphics and adaptive SoC products. AMD expects the acquisition to be accretive to non-GAAP margins, non-GAAP EPS and free cash flow generation in the first year. o § Health/Nutrition/Agriculture⠀➾ # ⚓ New_Campaign_Calls_On_Biden_and_Becerra_to_‘Make_Meds Affordable’⠀⇛ “The choice is clear—it’s our communities or Big Pharma.” “No one should have to choose between buying groceries and paying for medications they need to survive.” # ⚓ WHO_Says_Covid_Still_Killing_‘Far,_Far_Too_Many’_as_Pharma Hoards_Vaccine_Tech⠀⇛ Experts from the World Health Organization said Wednesday that global coronavirus deaths remain stunningly high two years into the pandemic as highly contagious variants—including Omicron and its relative—continue to circulate and possible new mutations loom. “At this point in the pandemic, when we have tools that can save people’s lives, this is far, far too many.” # ⚓ Global_Youth_Demand_EU,_UK_‘Unconditionally’_Back_Vaccine Patent_Waiver⠀⇛ Dozens of youth-led advocacy groups from around the world published an open letter Wednesday urging the European Union, the United Kingdom, Norway, and Switzerland to immediately end their opposition to a proposed patent waiver for coronavirus vaccines, which still remain out of reach for billions of people in poor countries. “Publicly funded vaccines should not be used to make pharmaceutical giants richer.” # ⚓ The_Benefits_of_Getting_the_Covid_Vaccine_as_a_Pregnant Black_Woman⠀⇛ I found out that I was pregnant in the summer of 2020 when most of the country was still in pandemic lockdown and racial justice protesters righteously filled the streets to exclaim that Black lives matter. It was a summer of nationwide anxiety and reckoning that touched everyone in different ways. # ⚓ If_Inequalities_Persist,_Africa_May_Not_Reach_70% Vaccination_Until_Late_2024⠀⇛ # ⚓ Many_Immunocompromised_People_Feel_Left_Behind_as_US_Lifts Pandemic_Measures⠀⇛ # ⚓ Back_to_Normal?_Many_Immunocompromised_People_Feel_Left Behind_as_U.S._Lifts_Pandemic_Measures⠀⇛ As U.S. health guidelines start to loosen as COVID- 19 cases fall from record-high levels of infection, we look at how there there are still millions of immunocompromised people who face acute risk of illness and feel they have received little to no guidance on how to stay safe in a prolonged COVID- 19 world. Pulitzer Prize-winning science writer Ed Yong of The Atlantic spoke to immunocompromised people for his new report and says, “While a lot of the world opens up, their world shuts down, and they feel left behind and abandoned by the government, by their friends, by their workplaces.” Yong notes immunocompromised people “want their lives back, too,” but are just asking for structural solutions to help keep them and non- immunocompromised people safe. # ⚓ Bald_eagles_show_signs_of_widespread_lead_poisoning⠀⇛ The study, which was published Thursday in the journal Science, evaluated eagles in 38 states, testing their bones, feathers, livers and blood for lead. Researchers found that 46 percent of bald eagles and 47 percent of golden eagles had chronic lead poisoning. # ⚓ Lead_contamination_found_in_Philadelphia_schools’_water: Report⠀⇛ An environmental group said Philadelphia’s school system needs to re-examine and rework its water pipes after a study found major lead contamination in school buildings. The report, which was released by the PennPIRG Education Fund, the PennEnvironment Research & Policy Center and the Black Church Center for Justice and Equality, found that 61% of outlets tested across 65 schools were tainted with lead. # ⚓ Extreme_Drought_Is_Crashing_Food_Production_Whether_Russia Invades_or_Not⠀⇛ Ukraine, a major grain exporter, has also been walloped by droughts in recent years—another climate story with international consequences that has been relatively under-covered. The country has long ranked among the most productive agricultural areas on Earth—under the old Soviet Union, it was the nation’s breadbasket—but climate change is dramatically decreasing output and, by extension, threatening the stability of food prices around the world. A report from the Atlantic Council last year emphasized the impacts of drought on Ukraine’s grain exports, noting that they had “fallen sharply year-on-year during the current season due to smaller harvests caused by severe drought conditions.” When an agricultural power as important as Ukraine suddenly starts producing and exporting much less food, it is a recipe for social dislocation, human suffering, and political unrest, both inside the country and beyond. Less production translates into higher prices. The price of food is something people everywhere care about, which makes it something journalists need to be talking about. # ⚓ Why_Doesn’t_Healthcare_Improve_Health?⠀⇛ However, I keep being surprised by intelligent and scientifically minded people outright refusing to hear the evidence against medicine being useful. That’s not to say evidence against any particular therapy. There are many things that obviously work, such as emergency intervention for losing a limb in a car crash, where “almost certain death” is the clear outcome. There are many things that obviously work from a statistical perspective, such as vaccination against diseases such as covid, hep A & B, polio, HPV, yellow fever, rabies, and the like. There are also many things that seem to work, with good mechanistic evidence and promising studies, such as PRP for various forms of soft-tissue injury, or prophylactic therapy for HIV. But this therapy-specific evidence is only more damming when viewed in the context of broader findings against medicine. Robin Hanson has written on this ad-nauseam, so I will let him do most of the talking. o § Integrity/Availability⠀➾ # ⚓ Scientists_Warn_That_New_AI-Generated_Faces_Are_Seen_As More_Trustworthy_Than_Real_Ones⠀⇛ As if the possibility that AI might already be conscious wasn’t creepy enough, researchers have announced that AI-generated faces have become so sophisticated that many people think they’re more trustworthy than actual humans. A pair of researchers discovered that a neural network dubbed StyleGAN2 is capable of creating faces indistinguishable from the real thing, according to a press release from Lancaster University. In fact, in a jarring twist, participants seemed to find AI-generated faces more trustworthy than the faces of actual people. # § Proprietary⠀➾ # ⚓ Russian_‘Minecraft_bomb_plot’_teen_jailed_for_five years⠀⇛ # § Security⠀➾ # ⚓ VMware_patches_critical_guest-to-host vulnerabilities [Ed: The security_problem_is VMware,_not_Linux]⠀⇛ In an advisory this week, VMware alerted users to guest-to-host vulnerabilities in the XHCI and UHCI USB controllers in its ESXi hypervisor, plus an important flaw fixed in NSX Data Center for vSphere. In all, five vulnerabilities were discovered in VMware’s ESXi, Workstation, Cloud Foundation (ESXi), and Fusion during the Tianfu Cup 2021, a Chinese vulnerability competition, by the country’s Kunlun Lab. Bugs that Kunlun discovered were disclosed privately to VMware – though last year China passed a new law ordering security researchers to reveal findings to the country’s Ministry of Public Security at least two days before anyone else. The vendor said it hadn’t seen any evidence the competition’s findings had been exploited in the wild. Patches have been issued, now it’s up to admins to schedule them. The vulnerabilities range from use-after-free() and double- fetch flaws that can be exploited to execute code on the host, to an old- fashioned denial of service (DoS). # § Privacy/Surveillance⠀➾ # ⚓ Head_of_Interior_Ministry_IT_center resigns_over_loss_of_data_device⠀⇛ An internal investigation concluded that the removable device in question had been destroyed, however the destruction of the device had not been properly documented. The device was destroyed at least four years ago. Stored on the device were archival copies of scans of historical documents involving family-related events. The disappearance of the device was discovered when a scanned file in the Population Register could not be accessed and needed to be replaced with an archived copy. The device containing the copies, however, could not be found. # ⚓ Majority_of_EU_states_want_EU-wide blanket_communications_data_retention⠀⇛ While the new German government has come out against indiscriminate data retention, the majority of EU governments have other goals. A diplomatic report to the German Foreign Office, published today by the news portal Netzpolitik.org, summarises the wishes and plans of EU governments on the issue of data retention. The EU Commission wants to take action following a pending decision by the European Court of Justice. # ⚓ Rights_Groups_Urge_Crack_Down_on_US Prison_Surveillance_Technology⠀⇛ Dozens of rights groups are demanding a crackdown on an artificial intelligence system used to eavesdrop on U.S. prisoners’ phone calls, after a Thomson Reuters Foundation investigation highlighted the risk of rights violations. Documents from eight states showed prison and jail authorities were using surveillance software called Verus, which scans for key words and leverages Amazon’s voice-to- text transcription service, to monitor prisoners’ phone calls. California-based LEO Technologies, which operates Verus, says it has scanned close to 300 million minutes of calls going in and out of prisons and jails in the United States, describing the tool as a way to fight crime and help keep inmates safe. # § Confidentiality⠀➾ # ⚓ Off-The-Record_Messaging_part_1: the_problem_with_PGP⠀⇛ This is a 4 part series about Off-The-Record Messaging (OTR), a cryptographic messaging protocol that protects its users’ communications even if they get [cracked]. # ⚓ Off-The-Record_Messaging_part_2: deniability_and_forward_secrecy⠀⇛ This is part 2 of a 4 part series about Off-The-Record Messaging (OTR), a cryptographic messaging protocol that protects its users’ communications even if they get hacked. In part 1 we looked at problems with common encrypted messaging protocols, such as PGP. We also considered two desirable properties for messaging protocols to have: confidentiality and authenticity. In this post (part 2) we’re going to look at two more important properties – deniability and forward secrecy – and see that many protocols fail to achieve them. We’ll then be ready to see how OTR works and how it provides each of confidentiality, authenticity, deniability and forward secrecy in parts 3 and 4. # ⚓ Off-The-Record_Messaging_part_3: how_OTR_works⠀⇛ This is part 3 of a 4 part series about Off-The-Record Messaging (OTR), a cryptographic messaging protocol that protects its users’ communications even if they get hacked. In parts 1 and 2 we looked at problems with common encrypted messaging protocols, such as PGP. We considered four desirable properties for messaging protocols to have: confidentiality, authenticity, deniability, and forward secrecy. In this post (part 3) we’ll see how OTR works and how it provides each of these properties, and then in part 4 we’ll delve into some of OTR’s key insights. # ⚓ Off-The-Record_Messaging_part_4: key_insights⠀⇛ This is the final part in a 4 part series about Off- The-Record Messaging (OTR), a cryptographic messaging protocol that protects its users’ communications even if they get hacked. In parts 1 and 2 we looked at problems with common encrypted messaging protocols, such as PGP. We considered four desirable properties of encrypted messaging protocols: confidentiality, authenticity, deniability, and forward secrecy. In part 3 we saw how OTR works and how it provides each of these properties, and in this final part we’ll delve into some of the protocol’s key insights. o § Defence/Aggression⠀➾ # ⚓ Numb_to_the_Real_Threats:_Why_are_We_Risking_Nuclear_War Instead_of_Striving_for_Peace?⠀⇛ Meanwhile, tensions continue to mount at the Ukraine-Russia border, as Putin moves more armaments and fleets around and the US flies its elite 82nd Airborne Division into standby mode in Poland, part of 3,000 US troops now deployed to the region. All of this has sent US nuclear hawks, sounding more and more like General ‘Buck’ Turgidson from Dr. Strangelove, chafing at the bit to justify the further escalation and acceleration of the so- called modernization of the entire US nuclear weapons complex. # ⚓ Conspicuous_Destruction:_Three_Generations_of_the_Military- Industrial_Complex⠀⇛ America’s war in Vietnam was waged during the Cold War in the context of what was then known as the domino theory and the idea of “containing” communism. Iraq and Afghanistan were part of the Global War on Terror, a post-Cold War event in which “radical Islamic terrorism” became the substitute for communism. Even so, those wars should be treated as a single strand of history, a 60-year war, if you will, for one reason alone: the explanatory power of such a concept. For me, because of President Dwight D. Eisenhower’s farewell address to the nation in January 1961, that year is the obvious starting point for what retired Army colonel and historian Andrew Bacevich recently termed America’s Very Long War (VLW). In that televised speech, Ike warned of the emergence of a military-industrial complex of immense strength that could someday threaten American democracy itself. I’ve chosen 2021 as the VLW’s terminus point because of the disastrous end of this country’s Afghan War, which even in its last years cost $45 billion annually to prosecute, and because of one curious reality that goes with it. In the wake of the crashing and burning of that 20- year war effort, the Pentagon budget leaped even higher with the support of almost every congressional representative of both parties as Washington’s armed attention turned to China and Russia. # ⚓ With_Its_Doomsday_Clock_at_100_Seconds_to_Midnight,_The Bulletin_of_the_Atomic_Scientists_Calls_for_Escalating_US Aggression_Against_Russia⠀⇛ Dropping the A-bombs By the time that the scientists at the top-secret Manhattan Project had developed the atomic bomb and the US military had worked out the logistics for deploying it, World War II was for all intents and purposes over. By early May 1945, Germany had unconditionally surrendered; in large part due to the efforts of the Red Army defeating the Nazi Wehrmacht, but at the horrific cost of 27,000,000 Soviet lives. The Japanese too had been defeated militarily and had agreed to “unconditional surrender” with the one caveat that Emperor Hirohito be spared. # ⚓ Fascism_is_a_Fire_That_Burns_Down_the_Entire_House⠀⇛ Even though the other side is a minority in Canada, there were still many who came out to support the “Freedom Convoy.” They not only convened in parks. They were everywhere. In all honesty, I haven’t felt that uneasy since I lived in the States. Trucks with enormous Canadian flags drove down every street blaring their horns which, for some of the vehicles, was deafening. I had already known that organizers of this convoy had a history of white supremacy and far-right ideologies. However, being present amongst them, it became very clear to this was not a movement, but a mob. The tactics they used were classic fascist bullying. Most didn’t care if people supported them or their cause or were interested in learning more. And most seemed more interested in intimidating people. What was also striking to me is how the authorities were friendly with many of them. I saw some of them chatting with them in a familiar and friendly manner. I’ve never seen that kind of thing happen at any of the protests I’ve attended that were anti-capitalist, against ecocide, antiwar or for Indigenous rights. # ⚓ The_Avoidable_Tragedy_of_Road_Deaths⠀⇛ After the shootings of a baby, a teenager, and two police officers in New York City, Mayor Eric Adams was quick to respond to the problem of gun violence. He gave a speech on the subject in January and laid out a comprehensive plan for combating violent crime. # ⚓ Coalition_Warns_Trump_and_GOP_Allies_Pose_‘Unprecedented’ Threat_to_Democracy⠀⇛ Donald Trump’s recent threat to unleash his supporters on major U.S. cities and suggestion that—if reelected—he would consider pardoning January 6 insurrectionists underscore the dire need to defeat the former president and his far-right GOP allies, both of which represent “a clear and present danger” to democracy. “Little has been done to hold Trump accountable or stop future presidents from similarly abusing their power.” # ⚓ In_Face_of_US_Claims,_Moscow_Says_“There_Is_No_‘Russian Invasion’_of_Ukraine”⠀⇛ Amid global demands for urgent diplomacy to de- escalate the Ukraine crisis, the Russian Ministry of Foreign Affairs on Thursday rebuffed allegations by the Biden administration—along with other Western governments and corporate media—that Russia intends to imminently invade its neighbor. “Rather than invoking a global order that no longer exists, the Biden administration should consider an agreement that offers a path out of this mess.” # ⚓ Opinion_|_What_Is_Going_to_Happen_in_Ukraine?⠀⇛ Every day brings new noise and fury in the crisis over Ukraine, mostly from Washington. But what is really likely to happen? # ⚓ Ex-U.S._Ambassador_to_USSR:_Ukraine_Crisis_Stems_Directly from_Post-Cold_War_Push_to_Expand_NATO⠀⇛ U.S. officials are accusing Russia of sending more forces to the Ukrainian border just days after Moscow announced it was pulling some troops back. This comes as Ukrainian authorities and Russian- backed separatists are both accusing the other side of violating a ceasefire in the eastern Donbas region of Ukraine. For more on the history behind the present crisis in Ukraine, we speak with one of the last U.S. ambassadors to the Soviet Union prior to the collapse of the USSR, Ambassador Jack Matlock, who says the U.S.-led expansion of NATO following the end of the Cold War helped lay the groundwork for the current standoff over Ukraine. He argues continued escalation could stoke another nuclear arms race, and lays out some of the parallels with the 1962 Cuban Missile Crisis. # ⚓ John_Pilger:_War_in_Europe_and_the_Rise_of_Raw_Propaganda⠀⇛ Marshall McLuhan’s prophecy that “the successor to politics will be propaganda” has happened.  Raw propaganda is now the rule in Western democracies, especially the US and Britain. # ⚓ America’s_Disastrous_60-Year_War⠀⇛ In my lifetime of nearly 60 years, America has waged five major wars, winning one decisively, then throwing that victory away, while losing the other four disastrously. Vietnam, Afghanistan, and Iraq, as well as the Global War on Terror, were the losses, of course; the Cold War being the solitary win that must now be counted as a loss because its promise was so quickly discarded. # ⚓ As_US_Renews_Support_for_Saudi_War_in_Yemen,_Civilian_Death Toll_Nearly_Doubles⠀⇛ Two parallel but very different meetings took place recently — one in search of peace, the other to plan more war. In Oman’s capital, Muscat, an official delegation headed by Ansar Allah, met with Omani and European officials to negotiate de- escalation and humanitarian assistance in Yemen. Meanwhile, the United States and the Saudi-led Coalition held meetings to plan a ground escalation in Sana’a and Hajjah province in Yemen’s southeast to coincide with airstrikes against residential neighborhoods in other cities throughout the north, which have killed and injured dozens of people and caused extensive damage to property and infrastructure. # ⚓ War_In_Europe_And_The_Rise_Of_Raw_Propaganda⠀⇛ Marshall McLuhan’s prophecy that “the successor to politics will be propaganda” has happened.  Raw propaganda is now the rule in Western democracies, especially the US and Britain. # ⚓ Ethiopia:_Amnesty_Accuses_Tigrayan_Forces_of_Rape_&_Murder in_Latest_Probe_of_War_Crimes_in_Conflict⠀⇛ Amnesty International is accusing Tigrayan forces of deliberately killing dozens of unarmed civilians and gang-raping dozens of women and girls in the northern Amhara region of Ethiopia. This comes as the Ethiopian government and Tigrayan rebel forces remain at war, and just last year Amnesty similarly accused the Ethiopian government of subjecting Tigrayan women and girls to rape, gang rape, sexual slavery, sexual mutilation and other forms of torture. “These are deliberate attacks which constitute war crimes and possibly may also constitute crimes against humanity,” says Amnesty’s Donatella Rovera, who led the investigation behind this most recent report. While Amnesty has been barred by the Ethiopian government from investigating these crimes on the ground, she says they have used satellite imagery to corroborate the testimonies of civilians who have escaped attacks by both Ethiopian government and Tigrayan rebel forces that began last July. # ⚓ Ukraine_banking_and_defense_platforms_knocked_out_amid heightened_tensions_with_Russia⠀⇛ NetBlocks metrics confirm the loss of service to multiple banking and online platforms in Ukraine, in a manner consistent with a denial of service attack. The incident comes amid heightened tensions with neighboring Russia. o § Transparency/Investigative Reporting⠀➾ # ⚓ FOIA_Lawsuit_Featuring_A_DC_Police_Whistleblower_Says_PD Conspired_To_Screw_Requesters_It_Didn’t_Like⠀⇛ It’s no secret government agencies love to screw with FOIA requesters. This is especially true when the responding agency doesn’t care for the requester’s attitude or thinks the release of information might lead to future negative reporting or embarrassment. o § Environment⠀➾ # ⚓ Pharmaceutical_pollution_of_the_world’s_rivers⠀⇛ Despite growing evidence of the deleterious effects on ecological and human health, little is known regarding the global occurrence of pharmaceuticals in rivers. Studies assessing their occurrence are available for 75 of 196 countries, with most research conducted in North America and Western Europe. This leaves large geographical regions relatively unstudied. Here, we present the findings of a global reconnaissance of pharmaceutical pollution in rivers. The study monitored 1,052 sampling sites along 258 rivers in 104 countries of all continents, thus representing the pharmaceutical fingerprint of 471.4 million people. We show that the presence of these contaminants in surface water poses a threat to environmental and/ or human health in more than a quarter of the studied locations globally. # ⚓ Climate_change_brings_thinner,_more_unstable_ice_to_the Great_Lakes⠀⇛ The lakes are also staying frozen for less time each year, and the ice that does form is more unstable thanks to shifting climate patterns and water temperatures, said Jia Wang, a researcher with the National Oceanic and Atmospheric Administration’s Great Lakes Environmental Research Laboratory. Average temperatures in the Great Lakes region rose 2.3 degrees Fahrenheit between 1951 and 2017, according to NOAA, and Wang said that warm water temperatures carry over from previous years, creating a feedback loop that builds every winter. It causes ice to form later into the next winter season and leaves less time for it to build up in a thick layer. # § Energy⠀➾ # ⚓ Study_Exposes_Climate_Claims_by_Big_Oil_as_Corporate Propaganda⠀⇛ While continuing to fuel the climate emergency over the past decade, oil and gas majors relied on misleading messages rather than actually taking action to transition to clean energy, according to research released Wednesday. “This study confirms what observers have always known about Big Oil’s climate pledges: They’re all hot air.” # ⚓ Texas’s_Power_Woes_Are_Just_the_Latest_Reminder_of the_Danger_of_Privatization⠀⇛ # ⚓ As_Trudeau’s_Crackdown_Shows,_No_Protest_Will_Ever_Be Worthy_Enough_for_the_Left⠀⇛ OTTAWA – If you were Canada’s prime minister, what would you be prepared to do to enforce Covid restrictions on large swaths of your population? No one need ask that question any longer. Now we know the answer. # ⚓ Canada’s_banking_industry_will_carry_out_emergency orders_to_stop_trucker_[blockade]⠀⇛ Canada’s banking industry says it will follow through with the federal government’s emergency orders targeting the trucker protesters as discussions on how best to implement them continue. The government published details late Tuesday on the requirements covering a wide range of the financial industry including banks, credit unions, insurance companies, portfolio managers and investment counselling services. # ⚓ Snoop_Dogg_Says_Death_Row_Records_Will_Be_an_NFT Label⠀⇛ Snoop joined a devoted Clubhouse room yesterday to discuss his purchase of the label. “Death Row will be an NFT label,” Snoop told fans. “We will be putting out artists through the metaverse. Just like we broke the industry when we was the first independent [label] to be major, I want to be the first major [label] in the metaverse.” That sentiment should come as no surprise to anyone who has followed Snoop Dogg over the last five years. The rapper is heavily invested in cryptocurrencies, the idea of the metaverse, and even outed himself as the person behind the wildly popular NFT speculation account, Cozomo di Medici. # ⚓ How_Do_NFTs_Harm_The_Environment?_The_Link Explained⠀⇛ Non Fungible Tokens — or NFTs for short — are everywhere in the [cryptocurrency] universe. Everyone wants in on the trend, from legendary tennis players like Serena Williams and Academy Award winner Reese Witherspoon to top music artists like Eminem and quintessentially chill dude Tony Hawk. Climate change activists are tailing the NFT wave too, but for a different reason. The inherent technology powering the whole NFT ecosystem is blockchain, predominantly Ethereum. And just like its more famous creation that the world calls cryptocurrency, the blockchain’s artsy side is an energy guzzler too. Just how significant the impact of digital art is, remains a topic of hot debate. # ⚓ Cryptocurrency,_NFTs_and_the_metaverse_threaten_an environmental_nightmare_–_here’s_how_to_avoid_it⠀⇛ As concerns rise and hearings are held in the US about the cryptocurrency industry’s effect on the environment, it’s time to address blockchain’s poor sustainability record. The first port of call should be changing how transactions on the blockchain operate – a move which could cut its energy usage by 99.99%. A cryptocurrency is a digital representation of value that, unlike traditional money, isn’t issued by any central bank or agency. Cryptocurrencies are powered by blockchain technology, which allows the exchange of virtual coins like bitcoin and ether. # ⚓ El_Salvador_leader_tells_‘boomer’_US_senators_to stand_down_over_bitcoin_adoption⠀⇛ El Salvador’s president rebuked several U.S. senators on Wednesday for introducing legislation targeting the Latin American country’s adoption of bitcoin as legal currency, referring to the lawmakers as “boomers.” # ⚓ FBI_to_form_new_cryptocurrency_unit⠀⇛ The FBI is forming a new team dedicated to cryptocurrency, according to the Department of Justice (DOJ). The new team will work closely with the National Cryptocurrency Enforcement Team, the DOJ announced Thursday. Prosecutor Eun Young Choi, who has a background in cyber-related crimes, will serve as the National Cryptocurrency Enforcement Team’s first director. # § Wildlife/Nature⠀➾ # ⚓ Humanity_Subsidizing_‘Our_Own_Extinction,’_Warns Study⠀⇛ Releasing a new study showing that world governments spend at least $1.8 trillion annually to subsidize activities which worsen the climate crisis, global subsidies experts on Thursday said leaders must eliminate or redirect the financial supports as part of an ambitious Global Biodiversity Framework at an upcoming summit in China. “Reforming the $1.8 trillion a year of subsidies that are harming the environment could make an important contribution towards unlocking the over $700 billion a year needed to reverse nature loss by 2030.” o § Finance⠀➾ # ⚓ Who_Will_Audit_the_State?⠀⇛ In a nutshell, here’s the way it works. The Legislature writes the laws and appropriates the money for the operation of the executive branch, which is defined in our Constitution as the governor, lieutenant governor, attorney general, secretary of state, and state auditor (Article VI, Section 1). Executive branch officers are charged to follow the law and “keep the public records of his office.” The governor is specifically charged to “see that the laws are faithfully executed.” Given the sheer size of government, one could credibly wonder who keeps an eye on what actually happens after the Legislature leaves town? And in that regard, it is the legislative auditor’s office that is charged with investigating and answering exactly that question for our part-time citizen legislators. # ⚓ The_Growing_Wealth_of_the_Billionaire_Class⠀⇛ This pandemic has had a devastating impact upon our country. Over 900,000 people have died from COVID, and tens of millions have been made ill. Many thousands of workers have lost their lives simply because they went about doing their jobs, while millions of other workers have chosen to find new employment paths. The education of young people, from child care to graduate school, has been severely disrupted. Elderly people have become increasingly isolated, fearful of catching the virus from grandchildren, friends or family. Mental illness is on the rise, as is drug addiction, alcoholism and domestic violence. These are very difficult times. # ⚓ Thoughts_on_Inflation,_After_the_January_CPI_Report⠀⇛ The basis for the belief that shipping problems were being fixed was both anecdotal accounts in the media and also the big increases in retail inventories reported for December. It seems stores had ordered (and received) lots of stuff they couldn’t sell. This is a context in which we might normally expect prices to fall, or at least not rise further. That turned out not to be the case. The price index for appliances rose 1.5 percent in January and is now 8.5 percent above its year ago level. The index for apparel rose 1.1 percent in the month putting it 5.3 percent above its year ago level. And, used vehicle prices rose 1.5 percent in January, and are now 40.5 percent above year ago levels. So, there is not much of a story of a turnaround there. # ⚓ For_New_York_Home_Care_Workers,_Fair_Pay_Is_Possible⠀⇛ # ⚓ Opinion_|_Inside_the_Campaign_to_Abolish_Poverty_Wages_in 25_States_by_2026⠀⇛ As the economy recovers from a global pandemic, many business owners are pointing to labor shortages caused by the “Great Resignation” as a source of frustration. # ⚓ Opinion_|_Afghanistan_on_the_Brink_of_Catastrophic Disaster⠀⇛ Gay rights, women’s rights—in reality, these are a nuisance to many U.S. conservatives, but purporting to protect these rights on the other side of the world is a great excuse to play war. # ⚓ ‘Cancel_It._Every_Penny’:_Poll_Shows_83%_of_Democrats_Want Biden_to_Nix_Student_Debt⠀⇛ Polling out Thursday reveals overwhelming support from President Joe Biden’s party for canceling student loan debt. “President Biden canceling student loan debt could be hugely consequential to millions of Americans facing significant financial burdens amidst the pain of rising costs.” # ⚓ Sanders_Rips_Into_Billionaires_for_Creating_“Oligarchic” Society_in_US⠀⇛ # ⚓ Big_Food_Producers_Are_Profiteering_Off_Inflation_—_and Bragging_About_It⠀⇛ o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Honduras:_The_Political_Context_Missing_from_Corporate Media⠀⇛ However, if one were to only read the corporate coverage of the issue, one would be complete without the political context for what has happened in Honduras since the 2009 coup. In fact, there is no mention at all from the Associated Press about what happened to former President Zelaya in 2009, the fact that Hillary Clinton led a coup against the elected leftist government which created the conditions for the rise of right-wing criminals like Hernández, but also directly led to the assassinations of activists such as Berta Cáceres and Afro-Indigenous leaders, among others. Given the utter failure of the corporate, mainstream media to properly frame the issue as part of a broader struggle between US-backed right- wing forces and the various left political movements opposing them, it seems an appropriate time to re-publish my piece on Honduras from 2015 which covers most of the critical issues. # ⚓ Moscow’s_package_deal_The_Russian_Foreign_Ministry’s response_to_Washington’s_security_proposals,_in_a_nutshell⠀⇛ On Thursday, February 17, the Russian Foreign Ministry issued a written response to Washington’s counter-proposals on security guarantees in Europe. Unlike the response Moscow received from the U.S. and NATO earlier this month, which wasn’t officially made public (though the full text was leaked to Spanish newspaper El Pais), the Russian Foreign Ministry published its 10-page commentary in full. Here’s what it says, in a nutshell.  # ⚓ The_professor_and_his_prophecies_Known_for_peddling_wild conspiracy_theories,_Valery_Solovey_is_now_wrapped_up_in_a felony_hate_speech_investigation⠀⇛ On Wednesday, February 16, law enforcement officers raided the Moscow home of political analyst Valery Solovey. Solovey and his son Pavel were then taken to the Russian Investigative Committee for questioning. As it turns out, Solovey is considered a witness in a criminal investigation into felony hate speech. Solovey and his son were released late Wednesday evening after being questioned. According to unofficial reports, the felony investigation is connected to an anonymous Telegram account called “SVR General” — allegedly, Solovey may have been involved in creating content for this channel, which regularly criticizes the Russian authorities. Meduza recounts how Valery Solovey, a former professor at Moscow’s prestigious MGIMO University, became an extravagant political commentator known for his colorful (and increasingly wild) conspiracy theories. # ⚓ And_Just_Like_That:_Free_Market_Democracy!⠀⇛ That’s because “And Just Like That” is part of a vast communist conspiracy – only capitalist. I know because I obtained security-cam footage from a secret “study session” the girls held at the end of Season One. Here’s the transcript. And, so all you commie-queers can fully comprehend the danger we face, I’ve translated it into post-Soviet Marxist- Leninism. [Scene: corporate boardroom somewhere in Manhattan’s Financial District. Affixed to back wall is large flat-screen TV with sound off, tuned to news channel NY1, which broadcasts weather forecast. Seated at polished rainforest-wood table is Charlotte York Goldenblatt. Looking pertly at the screen, she turns as door opens, revealing group leader Carrie Bradshaw.] # ⚓ Trump_Donor_John_Malone_Could_Soon_Be_Calling_Shots_at CNN⠀⇛ What will CNN become under John Malone? # ⚓ Russian_court_re-sentences_father_of_top_Navalny_aide_to three_years_in_prison⠀⇛ A court in Russia’s Nenets Autonomous Okrug has overturned a three-year suspended sentence previously handed down to Yuri Zhdanov — the 67- year-old father of Alexey Navalny’s top aide Ivan Zhdanov — and replaced it with time in prison. This was reported by Zhdanov’s lawyer Vladimir Voronin on Thursday, February 17. # ⚓ Russia_expels_U.S._Deputy_Ambassador_Bartle_Gorman⠀⇛ Russia has expelled U.S. Deputy Ambassador Bartle Gorman from the country, RIA Novosti reported on Thursday, February 17, citing embassy spokesperson Jason Rebholz. # ⚓ Downhill_From_Here⠀⇛ # ⚓ Leaked_Audio_Exposes_Amazon’s_Anti-Union_Scare_Tactics⠀⇛ During a mandatory anti-union meeting on Wednesday, an Amazon official warned workers at the corporation’s biggest New York City warehouse that if they unionize, pay and conditions could become worse, with salary negotiations possibly starting at “minimum wage.” “It’s against the law and an unfair labor practice to make a threat of reprisal.” # ⚓ Just_6%_of_US_House_Seats_Expected_to_Be_Competitive_Thanks to_Rigged_Maps⠀⇛ In a major blow to the democratic principle that lawmakers are accountable to voters who can remove them from office, the vast majority of seats in the U.S. House of Representatives are becoming non- competitive—a trend that critics say threatens to exacerbate GOP extremism as incumbents in solidly red districts shift further right to fend off more reactionary primary challengers. Several months into the decennial redistricting process, 335 congressional districts have been redrawn as of Thursday. Just 27 of them are considered competitive—meaning neither Democrats nor Republicans have an advantage of more than five points—according to FiveThirtyEight. # ⚓ Opinion_|_It’s_Settled_That_Israel_Is_Committing_the_Crime of_Apartheid—Now_What_Should_We_Do_About_It?⠀⇛ When Amnesty International released its report “Israel’s Apartheid Against Palestinians: Cruel System of Domination and Crime Against Humanity” earlier the month, it was clearly part of a rapidly expanding trend. Palestinian human rights defenders, members of Congress and faith leaders in the United States, academics, and activists of the Palestinian rights movement around the world have long recognized and condemned Israeli apartheid, and called for accountability. # ⚓ Trump_Acolyte_LePage_Given_Green_Light_to_Run_for_Third Term_in_Maine⠀⇛ Former Maine Gov. Paul LePage, a far-right Republican who made openly racist comments about immigrants in the state and compared himself to former President Donald Trump during his time in office, has officially been approved to run for a third term. “We can’t let Paul LePage drag us backward once again.” # ⚓ Telex_asked_Orbán_allies:_have_power_and_influence_changed Viktor_Orbán?⠀⇛ # ⚓ Broadcasters_Go_Against_Big_Tech_With_Congress_Forcing Negotiations⠀⇛ The president of the National Association of Broadcasters is urging Congress to pass legislation that would allow broadcasters and news organizations to negotiate with Big Tech platforms on terms to host their content. Curtis Legeyt said at an event hosted by The Media Institute Tuesday that the Journalism Competition and Preservation Act, sponsored by Senator Amy Klobuchar, D-Minnesota, would help smaller broadcasting stations get their share of the pie and allow them to compete against larger players in the industry. # ⚓ Twitter_opens_access_to_anti-abuse_tool_for_millions_of users⠀⇛ ‘Safety Mode’ temporarily blocks accounts for seven days for using potentially harmful language — such as insults or hateful remarks — or sending repetitive and uninvited replies or mentions. The ‘Safety Mode’ tool is now available in beta for more users across English-speaking markets, including the US, the UK, Canada, Australia, Ireland and New Zealand… # ⚓ Christopher_Parsons_Delivers_Testimony_to_the_Standing Committee_on_Access_to_Information,_Privacy_and_Ethics⠀⇛ Citizen Lab senior research associate Dr. Christopher Parsons provided the following briefing on Monday, February 14, 2022 to the House of Commons’ Standing Committee on Access to Information, Privacy, and Ethics, regarding the collection and use of mobility data by the Government of Canada. # ⚓ Scam_Review:_Big_Tech_Bullshit⠀⇛ This is a post that I will probably come to regret writing and publishing in the future. The reason for that is simple. This post is going to make a lot of former, current and potentially future co- workers feel like idiots. That’s because the topic for this post is scams being pushed by our friends in Big Tech. So it gets somewhat awkward when you realize that I work in tech and plan to continue doing so for the foreseeable future. It gets way more awkward if you know that when it comes to tech scams / fads, nobody is more susceptible to falling for this stuff than people who work in tech. That’s where all this stuff starts and builds momentum after all. Without buy in from the tech community, almost none of this garbage would exist. Today we are going to briefly touch on three tech fads which are actually scams and I’m going to attempt to give you all a brief explanation as to why they are scams. So without further adieu lets get started. # ⚓ Islamists_Take_Advantage_of_Political_Correctness⠀⇛ As reported by the Organization for Security and Co-operation in Europe, at least a quarter, though arguably much more, of all hate crimes registered in Europe in 2020 were anti-Christia—representing a 70 percent increase in comparison to 2019. As explained by Raymond Ibrahim, Christianity is, furthermore, the religion most targeted in hate crimes, with Judaism at a close second. # ⚓ Welcoming_the_New_Zealand_Government_to_Have_I_Been_Pwned⠀⇛ Continuing the march forward to provide governments with better access to their departments’ data exposed in breaches, I’m very pleased to welcome the 28th national government onto Have I Been Pwned – New Zealand! They’ll join the other govs around the world that have complete free access to breach information impacting their gov domains and TLDs. # ⚓ US,_Allies_Warn_Possible_Russian_Cyberattacks_Could Reverberate_Globally [iophk: Windows TCO]⠀⇛ “It’s not hypothetical,” Monaco said, pointing to the June 2017 “NotPetya” virus, engineered by Russia’s military intelligence service, the GRU. The virus initially targeted a Ukrainian accounting website but went on to hobble companies around the world, including Danish shipping giant Maersk and U.S.-based FedyEx. “Companies of any size and of all sizes would be foolish not to be preparing right now,” Monaco said. “They need to be shields-up and really be on the most heightened level of alert.” # ⚓ As_Russia_amasses_troops,_Ukraine_battles_another_threat: Digital_warfare [iophk: Windows TCO]⠀⇛ A new wave of cyber operations began in earnest Jan. 13, when computers in Ukraine started showing signs of the first serious hacking campaign since Russia’s troop buildup. Computers at dozens of Ukrainian organizations, including nonprofit groups, information technology companies and more than 70 government websites, were infected with malicious software that appeared to be ransomware, a common criminal tactic to lock up computers. # ⚓ US_says_Russian_[crackers]_targeted_defense_contractors [iophk: Windows TCO]⠀⇛ The U.S. intelligence community says that Russian- sponsored actors have been targeting defense contractors for at least the past two years and in some cases have gained access to sensitive information. In an alert released Wednesday, the FBI, National Security Agency (NSA) and Cybersecurity and Infrastructure Security Agency (CISA) said they had observed “regular targeting” of contractors from at least January 2020 through this month. o § Misinformation/Disinformation⠀➾ # ⚓ Spotify_reportedly_paid_$200_million_for_Joe_Rogan’s podcast⠀⇛ Spotify reportedly paid Joe Rogan at least $200 million to commit to podcasting on the platform exclusively for three and a half years, according to a New York Times report. That number, while astronomical, is double what had previously been reported in The Wall Street Journal as Rogan’s deal price — $100 million — and has continued to be used widely in the media without correction from Spotify’s team. This news comes after a volatile month for the audio company and one in which musicians, podcasters, employees, and the medical community scrutinized the company’s work with the controversial podcaster. In January, a group of medical community members penned a letter to the company asking it to remove a Rogan episode they said peddled COVID-19 misinformation. Musician Neil Young read that letter and subsequently pulled his catalog from the platform in response. # ⚓ Twitter_is_bringing_pinned_DMs_to_everyone⠀⇛ Twitter is now rolling out pinned DMs, the company announced Thursday. The feature was previously only available to Twitter Blue subscribers, but it’s now coming to everyone on Android, iOS, and the web. The feature doesn’t seem to be fully rolled out just yet. I have access to it on the iOS app, but not on Twitter’s web app. On the iOS app, you can swipe to the side on a conversation to reveal a pin, and if you tap that, the conversation will be moved to a new “Pinned conversations” section at the top of your DM inbox. o § Censorship/Free Speech⠀➾ # ⚓ Whatever_Problem_EARN_IT_Is_Trying_To_Solve,_It_Doesn’t⠀⇛ I’ve already talked about the potential 1st Amendment problems with the EARN IT Act and the potential 4th Amendment problems with it as well. But a recent post by Riana Pfefferkorn at Stanford raises an even bigger issue in all of this: what actual problem is EARN IT trying to solve? # ⚓ Blackburn_&_Blumenthal_Introduce_Terrible,_Dangerous_Bill To_Make_Sure_Children_Are_Constantly_Surveilled_Online⠀⇛ Senator Richard Blumenthal is apparently a bottomless well of terrible internet regulation ideas. His latest is yet another “for the children” bill that will put children in serious jeopardy. This time he’s teamed up with the even worse Senator Marsha Blackburn to introduce the Kids Online Safety Act, which as the name suggests is full of a bunch of overbearing, dangerous nonsense that will not protect children at all, but will make them significantly less safe while giving clueless, authoritarian parents much more power to spy on their kids. # ⚓ Senator_Blumenthal:_Dismissing_All_Critics_Of_EARN_IT_As ‘Big_Tech_Lobbyists’_Shows_Your_Unwillingness_To_Recognize The_Massive_Problems_In_Your_Bill⠀⇛ In the past, whenever Senator Richard Blumenthal has been called out for his many terrible legislative ideas regarding regulating technology and the internet, he has a habit of dismissing all of the concerns by claiming the complaints are only coming from “big tech lobbyists.” He did this a few years ago with FOSTA, which has since proven to be exactly the disaster many of us warned Senator Blumenthal about at the time. This time around, he’s going straight to the same playbook again, and it’s good to see that he’s getting some pushback. Nathalie Maréchal, from Ranking Digital Rights has published a great piece over at Tech Policy Press: No, Senator Blumenthal, I am not a Big Tech Lobbyist. # ⚓ Opinion_|_The_Story_of_How—Many_Years_Ago—I_Unbanned_Maus⠀⇛ Sometimes life has a way of making you realize things about yourself. Recently, I discovered that an urge of mine, almost four decades old, had been the very opposite of that of a rural Tennessee school board this January. In another life, I played a role in what could be thought of as the unbanning of the graphic novel Maus. # ⚓ Sundance_Film_Festival_Under_Fire_For_‘Islamophobia’⠀⇛ The film, which The Wrap called a “hot-button documentary,” is called Jihad Rehab. The 2022 Sundance program says that it “film focuses on several men — detained in Guantanamo for years without charge by the United States — after they are placed in what’s billed as the world’s first rehabilitation center for extremists.” The reminder that they were “detained without charge,” with no mention of 9/11 or the global jihad, is the first tipoff that this is not exactly a “right-wing” presentation, which is how it got to Sundance in the first place. But that didn’t stop it from running afoul of the Thought Police. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ Tactical_acquittal⠀⇛ Holding a citizen accountable by law in a foreign country is an upbeat challenge. WikiLeaks founder Julian Assange is a case in point. Hussain is a proclaimed fugitive since 2015 from the anti- terrorism courts in Pakistan on the charges of murder, targeted killings, treason, inciting violence and hate speeches. But the prosecution couldn’t carry the case under British law. This necessitates a legal valve, which should be analysed at the outset whether framing of charges will stand in a foreign court of law or not. No point in merely playing to the gallery. # ⚓ The_Belmarsh_Tribunal_NYC:_Shut_down_Guantanamo._Free Assange_—_February_25⠀⇛ Classified documents leaked by Chelsea Manning and published by Wikileaks in 2011 revealed the grim contours of the US regime of detention and torture at Guantánamo. Many prisoners — among them a journalist from Al Jazeera — were held for years despite officially posing no threat to the US. Many developed severe mental health problems as a result of their treatment. Some committed suicide. But, today, it is not the perpetrators who face persecution, but the whistleblowers. In April this year, Julian Assange will enter his third year of detention at HMP Belmarsh — a maximum-security prison, sometimes referred to as “Britain’s Guantánamo”, that was infamously used to detain terrorist suspects without trial — as he seeks to appeal a court decision to extradite him to the US. That is why the Progressive International is **bringing the Belmarsh Tribunal to the belly of the beast. On 25 February 2022, at the People’s Forum in New York City, we will convene legal experts, UN representatives, whistleblowers, journalists, and many others to investigate and expose the crimes of the so-called War on Terror, to seek justice for its victims, and to demand the closure of the concentration camp at Guantánamo Bay. o § Civil Rights/Policing⠀➾ # ⚓ Mexican_Forces_Evict_Indigenous_Activists_Who_Took_Over Water_Bottling_Plant⠀⇛ # ⚓ Free_Crack_Pipes?_Time_to_Pardon_Tommy_Chong⠀⇛ While “harm reduction” is the stated goal of  that federal program, the Biden administration continues to ignore the vast harms caused by federal drug prohibitions, despite record numbers of deaths from drug overdoses last year. The latest federal drug war farce should be a reminder of one of the biggest drug war publicity stunts of this century. On the eve of George W. Bush’s invasion of Iraq, Attorney General John Ashcroft announced the most decisive federal attack ever made on pipes and bowls often used for smoking marijuana, tobacco, and other substances. Ashcroft bewailed, “The illegal drug paraphernalia industry has invaded the homes of families across the country without their knowledge.” Ashcroft did not offer any evidence that pipe sellers, unlike government agents, were planting evidence in people’s homes. # ⚓ Time_for_a_Show_Trial⠀⇛ The Washington Post reported that Rep. Adam Schiff (D-CA) said that the House’s Select Committee on January 6th will hold public hearings to “tell the whole story” about the attack. “I think we will want [public hearings] to tell the whole story,” Schiff said. “Security at the Capitol, the intelligence leading up to the attacks, lack of intelligence, the role of social media, the former President’s role, the role of those around him, and tell it in an era fashion so the public knows exactly what’s going on.” Evidence is mounting that the attack on the U.S. Capitol on January 6th was not an isolated, impulse act by well-meaning, if uninformed, citizens.  No, January 6th was but one aspect of an incoherent, poorly planned and even more poorly executed coup d’état.  It failed and Joe Biden became president. # ⚓ The_Josh_Hawley_Mug:_It_Makes_Him_An_Asshole,_But_Shouldn’t Make_Him_A_Copyright_Infringer⠀⇛ Josh Hawley, the waifish fascist Senator from Missouri, has made it onto our pages several times in the past. When he’s not advocating breaking up Twitter because he doesn’t like how a private company is run (fascist), or breaking up lots of other companies he simply disagrees with (fascist), you can typically find him pretending the First Amendment works the exact opposite of how it does in reality or explaining in published books and newspaper pages how much he’s been silenced and canceled. It might all look very stupid on its face, but it isn’t. It’s actually quite diabolical.   # ⚓ California_Sheriff,_US_DOJ_Sued_For_Seizures_Of_Cash Generated_By_Legal_Pot_Businesses⠀⇛ A lawsuit filed against both California and federal law enforcement agencies claims the San Bernardino County Sheriff’s Department is exploiting the disagreement between state and federal marijuana laws to stop and seize cash being transported from legal marijuana dispensaries. # ⚓ Opinion_|_It’s_Time_to_Get_Loud_on_Abortion_Rights⠀⇛ Earlier this year, a small group of women and I gathered to post artwork around Washington, D.C. We were celebrating the 49th anniversary of Roe v. Wade, which protected women’s constitutional access to abortion. # ⚓ 55+_US_Prosecutors_Join_in_‘Inexorable_Conclusion’_That Death_Penalty_Must_End⠀⇛ A bipartisan group of 56 elected prosecutors came together in a new joint statement calling for “a more fair, just, and accountable criminal legal system” in the U.S. that includes bringing a permanent and complete end to the death penalty. “It is time to work together toward systemic changes that will bring about the elimination of the death penalty nationwide.” # ⚓ Opinion_|_San_Francisco_Rape_Kit_Controversy_Will_Have Chilling_Repercussions⠀⇛ This week, San Francisco District Attorney Chesa Boudin came forward with a stunning claim: That the San Francisco Police Department’s crime lab uses DNA evidence obtained from rape kits and entered into a DNA database to try to identify suspects in other crimes. # ⚓ Amazon_Warehouse_Workers_Want_to_Feel_Safe⠀⇛ Edwardsville, Ill.—On December 10, a tornado flattened an Edwardsville, Ill., Amazon distribution center building, killing Etheria S. Hebb and five others. Arnetra Rhodes, 18, didn’t learn Etheria was her cousin until her mother and family began to mourn. After Rhodes found out what happened, she couldn’t shake the feeling that Etheria should still be alive. “It would’ve been different if they let them know what’s going on.… I know that they heard the sirens.” Rhodes told me. # ⚓ Opinion_|_Africa-EU_Summit_Will_Not_Be_Successful_Unless_It Addresses_the_Abhorrent_Neo-Colonialism_of_Past_and_Present⠀⇛ The climate crisis does not exist in a vacuum. It cannot be solely seen through a physical and environmental lens as it has been both created by a particular group of people, and has been impacting certain communities disproportionately. # ⚓ Amir_Locke’s_funeral:_Mom_says_son_was_‘executed,’_Sharpton delivers_powerful_eulogy⠀⇛ The Rev. Al Sharpton delivered a powerful and emotional eulogy at Thursday’s funeral for Amir Locke, a 22-year-old who was shot and killed by Minneapolis police officers executing a “no-knock” search warrant. Locke, who was fatally shot on Feb. 2, was not named in the “no-knock” warrant. # ⚓ No-Knock_Warrants:_What_Are_They_and_How_Are_They_Used?⠀⇛ “They’re not functionally doing anything to keep people safer or reduce crime. They are, in fact, doing more harm than good by allowing law enforcement to largely enter people’s homes with impunity, without any consequence, with little oversight, and with little reason or rationale that actually has any impact on reducing harm,” says Katie Ryan, chief of staff for Campaign Zero, an organization focused on reducing police violence, including putting an end to no-knock raids. The practice has received renewed attention in recent years, especially after a 2014 incident in which police entered a Georgia home with a no-knock warrant and threw a grenade into a 19-month-old’s crib. The grenade left the toddler in an induced coma with severe burns. The suspect and the drugs they were searching for were not found in the home. # ⚓ Employers’_uphill_fight⠀⇛ Yes, but: 61% of teleworkers are working from home because they’re choosing to, per a new Pew Research study. Just 38% are home because their workplaces are closed or unavailable. There’s a disconnect between leadership and rank- and-file workers. Executives are three times as likely as employees to want to return to work, per a recent Future Forum survey. # ⚓ Court_frees_brother_who_confessed_to_killing_social_media star_Qandeel_Baloch⠀⇛ The brother of murdered social media star Qandeel Baloch has been freed by a Pakistan appeals court, three years after he was convicted of killing her for “bringing dishonor” to the family. Baloch’s murder in 2016 sparked a national outcry and promoted changes in the country’s so-called ‘honor killing’ laws. Waseem Baloch’s lawyer, Sardar Mehmood, confirmed the acquittal with CNN Tuesday but did not provide further details. A court order has not yet been made public. # ⚓ Christian_killed_by_a_group_of_Muslims_in_Lahore⠀⇛ Akhtar Bhatti, Pervez’s uncle, told AsiaNews that the next day a group of 150 to 200 Muslims came to the Christian area of ​​Lahore, some with guns, and started insulting and beating people, including Pervez. Despite his uncle’s attempts to stop the beating, the attackers dragged Pervez away to torture him with sticks and bricks, threatening that they would not leave him alive. # ⚓ Syrian_wanted_to_kill_sister_in_Germany:_“If_I_can’t_kill my_sister_today,_I’ll_do_it_tomorrow._If_I_can’t_do_it tomorrow,_I’ll_do_it_the_day_after_tomorrow…”.⠀⇛ The slender, small defendant (18 years, 1.60 metres) who is said to have said these words hides his face behind a briefcase. Since Friday, he has been standing trial for attempted murder at the Dortmund Regional Court. # ⚓ Police_Destroy_FOUR_MILLION_Bottles_of_Beer⠀⇛ Concerned about the government overstepping its bounds and asserting increasing control over aspects of life it has no business interfering with? You should be. And in many parts of the world, governments are providing daily object lessons in what happens when citizens allow self- serving, power-mad officials to arrogate too much power to themselves and overstep all rational restraints. In Nigeria on Wednesday, for example, a state government destroyed nearly four million bottles of beer. Four million bottles of beer, gone, sacrificed to fanaticism and the brutal arrogation of power by unfeeling elites. # ⚓ Union_Busting:_What_Are_Some_of_the_Most_Common_Tactics Employers_Use?⠀⇛ The blowback to Starbucks’ actions isn’t surprising when you look at the numbers. A 2021 Gallup poll puts public approval of unions at 68%, and for people aged 18-34, the approval rating sits even higher at 77%. In the past year alone, graduate student workers all over the country have launched union drives, won union recognition, or secured contracts. Tech workers at Google, congressional staffers on Capitol Hill, ACLU employees, and the staff at several major museums have all waged their own union campaigns. Even social media influencers now have the option to join the union wave. But no matter how popular the public perception of unions might be, winning union recognition remains an uphill battle. Employers determined to prevent their workers from successfully unionizing typically rely on a series of anti-union tactics often referred to as “union busting.” Teen Vogue spoke with Mindy Isser, a Philadelphia- based labor organizer, and Dr. John Logan, the department chair of labor and employment studies at San Francisco State University, to cover some of the basic union-busting tactics and tools employers use to crush unions. # ⚓ A_Student_Sleuth_Found_Evidence_that_Our_University Practices_Reverse_[sic]_Racism._Here’s_Why_I_Advised_Him_Not to_Publish_It⠀⇛ Daniel explained that he and his friend wanted to find a measure of academic achievement that they could track statistically. A student’s GPA is not public information, but the Dean’s List is; so they were able to use that as a discrete variable—Dean’s List, yes or no—as a rough proxy for achievement. Daniel explained to me that it would have been better to use a continuous variable (like GPA), but he and his friend had to work with what they had. Daniel explained that he and his friend had performed various kinds of statistical analysis on the data, and had concluded that admission to the honors program was closely related to Dean’s List status within certain groups. However, there were large differences in acceptance rates across those groups. Overall, he told me, the factor that explained the most variance in admissions outcomes was (as he’d suspected) the race or ethnicity of the applicant. The patterns were quite stark. African Americans who weren’t on the Dean’s List had a better overall chance of being admitted to the honors program than whites or Asians who were on the Dean’s List. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Cloud_Innovation_Ltd_loses_appeal_against_AFRINIC⠀⇛ TL;DR — AFRINIC has won. A dramatic legal battle that started in March of last year, can be probably said to be concluded now. # ⚓ Who_is_squatting_IPv4_addresses?⠀⇛ For the case of this post, I will define IP address squatting as “using IP addresses that are not RFC1918 defined and not your unicast space issued by a RIR”. The first thing that instantly comes to mind is Cloudflare obtained the addresses 1.1.1.1 and 1.0.0.1 to run a DNS resolver on, but had to fight back against a huge amount of network and home routers squatting on those addresses internally (I do also wonder if the last unicast / 24 block has similar issues) This problem is not that surprising though, your local friendly sysadmin might be able to tell you of a story where they have caught their colleagues, customers, or even parents squatting on addresses. But how big of an issue is this? If only we had a large amount of well known IP address blocks that we can make a safe bet on not being used. o § Digital Restrictions (DRM)⠀➾ # ⚓ Gift_Of_Sight_Stolen_As_Medical_Implant_Company_Implodes⠀⇛ Techirt has long discussed how in the modern era, the things you buy aren’t actually the things you buy. And the things you own aren’t actually the things you own. Things you thought you owned can be downgraded, bricked, or killed off entirely without much notice. That game console with backward compatibility? It no longer has backward compatibility. That smart home hub or smart speaker at the heart of your living room setup you’ve enjoyed for years? It not long works. The movies and books you thought were permanently in your personal catalog? Sorry, they aren’t anymore. That perfectly good two-year-old phone? It no longer gets security updates, putting you and your data at risk. o § Monopolies⠀➾ # § Copyrights⠀➾ # ⚓ Apple_v._Corellium_Demonstrates_a_Clear_Example_of Fair_Use_–_Public_Knowledge⠀⇛ Public Knowledge has been tracking the lawsuit by Apple against Corellium for a while. Corellium is a company that offers various services for software developers and security researchers. Some of these involve creating virtual iPhones for testing and research purposes, which involves making copies of Apple’s iOS software. Apple sued, arguing both that Corellium violated the “anticircumvention” provisions of the Digital Millennium Copyright Act (DMCA) by simply accessing iOS, and substantive copyright law, by making new copies of it. # ⚓ Auguste_Rodin’s_Sculptures_Are_In_The_Public_Domain; 3D_Scans_Of_Them_Should_Be,_Too⠀⇛ Auguste Rodin is without doubt one of the greatest sculptors in history. Equally without doubt, his works are now in the public domain, since he died in 1917. Unfortunately, the situation in France is a little more complicated, for reasons the artist and public domain campaigner Cosmo Wenman explains: # ⚓ EFF_to_Court:_Security_Research_Is_a_Fair_Use⠀⇛ Apple is putting that principle at risk in its lawsuit against Corellium. Corellium created a virtualization of Apple’s iOS operating system that allows developers and researchers to test iOS for vulnerabilities without having to get permission from Apple or pay for the privilege of finding flaws in the system. Apple sued, and lost in district court on fair use grounds. Apple’s hoping for a different ruling on appeal. It shouldn’t get one. EFF, along with Public Knowledge and a number of security experts, filed an amicus brief with the court explaining one reason why: the public’s interest in greater security, more innovation, and more competition in mobile software. We can’t protect ourselves from security flaws if independent testers aren’t allowed to find them. Companies use legal threats, like a threat of suing over copyright infringement, to silence researchers and keep users from knowing that there’s something wrong with their devices. Without meaningful protection from such claims, organizations like Corellium cannot develop research tools, researchers cannot conduct independent testing, and the public loses out on the benefits of innovation and competition to enhance security. # ⚓ Twitter_and_Facebook_Must_Speak_Out_Against_Ghana’s Repulsive_Anti-LGBTQI+_Bill⠀⇛ Both Twitter and Facebook have invested heavily in Ghana, which holds itself out to be a constitutional democracy with a strong commitment to human rights. Twitter announced last year it was establishing a headquarters in the Ghanaian capital Accra, citing Ghana as “a supporter of free speech, online freedom, and the Open Internet.” Meanwhile Meta (née Facebook), has long trumpeted its success in bringing connectivity to Ghana through programs like Free Basics and Express Wi-Fi. But now, the Ghanaian parliament has introduced the “Promotion of Proper Human Sexual Rights and Ghanaian Family Values Bill,” a draconian measure that would undermine the Ghanaian Constitution’s core guarantees of freedom of thought and expression. Pulling no punches in a press statement, a group of professors, journalists, and advocates described the bill as “an Orwellian nightmare fraught with stigmatization, bigotry, intolerance, repression, authoritarianism, violation of the fundamental human rights of LGBTQ+ persons and those who defend their human rights, false piety, cruelty to, and lack of empathy, for difference in our society.” While Ghanaian law has long criminalized same-sex sexual activities, the new proposal goes much further by threatening up to five years in jail for publicly identifying as LGBTQ or “any other sexual or gender identity that is contrary to the binary categories of male and female.” The sentence increases if the offending person expresses their gender beyond or identifies outside of the so-called “binary gender.” # ⚓ Episode_6:_Open_Culture_VOICES_–_Biyanto_Rebin⠀⇛ # ⚓ Police_Arrest_Man_For_Uploading_‘Parasite’_Movie_Edit to_YouTube⠀⇛ Police in Japan have just arrested another man for posting 10-movie summaries to YouTube including the hit Korean drama ‘Parasite’. The 48-year-old gave a media interview last year talking about his ‘legal’ work but then complained that it had been edited down, carried on with his work, and then got raided. # ⚓ Supreme_Court_Rejects_Appeal_of_Sports_Streaming_Site Rojadirecta⠀⇛ Popular sports streaming site Rojadirecta will remain outlawed in Spain for now. The Supreme Court has denied a hearing of the site’s appeal against a previous order which required the site to block Spanish visitors. Meanwhile, criminal prosecution against several Rojadirecta defendants is also about to start. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 11406 ➮ Generation completed at 02:43, i.e. 135 seconds to (re)generate ⟲